Lawyers for The Sun newspaper in the UK will ask for an injunction banning the identity of the well-known footballer at the centre of a controversial privacy ruling to be lifted, the newspaper said on its website.
The move follows a Scottish newspaper's decision to identify the star at the weekend.
British Prime Minister David Cameron has said that banning newspapers from naming stars at the centre of injunctions while the information is widely available on the internet is both "unsustainable" and "unfair".
Speaking to ITV1's 'Daybreak', Mr Cameron indicated that he knew the identity of the footballer linked to a controversial privacy case "like everybody else".
'Big Brother' star Imogen Thomas had a relationship with the married star, referred to as CTB in court documents.
Newspapers are prevented from identifying the player by a court injunction, although tens of thousands of Twitter users have named him.
Mr Cameron said: "It is rather unsustainable, this situation, where newspapers can't print something that clearly everybody else is talking about, but there's a difficulty here because the law is the law and the judges must interpret what the law is.
"What I've said in the past is, the danger is that judgments are effectively writing a new law which is what Parliament is meant to do.
"So I think the government, parliament, has got to take some time out, have a proper look at this, have a think about what we can do, but I'm not sure there is going to be a simple answer."
Mr Cameron suggested that one route might be to strengthen the Press Complaints Commission.
"It's not fair on the newspapers if all the social media can report this and the newspapers can't, so the law and the practice has got to catch up with how people consume media today," he said.
In a statement on The Sun's website, a spokesman said: "Following publication on the front page of a Scottish newspaper it is clear this injunction is unworkable.
"When the Prime Minister says on breakfast television that he knows the identity of the footballer, it is time for the courts to do the right thing and end a situation where readers of some newspapers but not others are allowed to know the worst-kept secret in the country.
"We have asked our lawyers to make an application at the High Court and await the outcome with great interest."
Last week, a gagging order obtained by former Royal Bank of Scotland chief Fred Goodwin was partially lifted by the High Court after allegations that he had an affair were made public by Liberal Democrat peer Lord Stoneham of Droxford in the House of Lords.
An urgent parliamentary question to Culture Secretary Jeremy Hunt has also been accepted for 3.30pm today.
The question from Culture Select Committee chairman John Whittingdale asks Mr Hunt to set out the Government's position on "granting and enforcement" of privacy orders.
The Sunday Herald newspaper published a thinly-concealed front page photograph of the player yesterday.
They printed his face with his eyes blacked out and the word "censored" written over the top.
Beneath the picture they wrote: "Everyone knows this is the footballer accused of using the courts to keep allegations of a sexual affair secret."
In an editorial, the Sunday Herald - the first mainstream publication to apparently identify the player - also said it was "unsustainable" for newspapers not to be able to print information which is available on the internet.
The Attorney General Dominic Grieve was aware of the report, but "hasn't received any complaints or referrals from any parties or by any court", a spokesman said.
Paul McBride QC, the Sunday Herald's legal adviser, said it was unacceptable for unelected judges to make the decisions to grant injunctions in private.
Speaking on BBC Radio Scotland's Good Morning Scotland programme, Mr McBride said there needed to be a debate about the way forward over granting privacy injunctions.
He said: "Parliament now have to look at this issue. We can't have unelected judges making these decisions in private when we have the internet out there where everyone can access the information they're trying to keep secret.
"We had the absurd position this week of even MPs in our democratically elected Parliament being threatened with potential contempt of court by using their parliamentary privilege to name people. That's not acceptable any more."
The footballer obtained an injunction preventing The Sun from revealing his name last month and has now launched proceedings against Twitter and "persons unknown".
Lawyers acting for CTB are asking Twitter for information about the people who "may have breached a court order".
A Twitter spokesman said they were unable to comment on the issue.
Scottish First Minister Alex Salmond added it would be "extremely foolish" for the Attorney General in England to try to start proceedings against a Scottish publication.
"I think it would be very, very unlikely that an Attorney General would be as foolish as to do so," he told the BBC Radio 4 'Today' programme.
"I think the political issue is whether it is tenable to pursue this sort of injunction.
"I would have thought there is an increasing view it is untenable to do so. There is a whole question of what is of interest to the public and what is in the public interest, which can often be different things.
"But the law essentially is a practical thing. It looks to me like English law and English injunctions are increasingly impractical in the modern world."
Mr Salmond ridiculed the idea that English court rules on any subject "should pertain across the planet".
Last week, the most senior judges in England and Wales were accused of trying to gag the media after criticising politicians who have deliberately disclosed the content of privacy cases covered by injunctions.
The Lord Chief Justice Lord Judge questioned whether it was a good idea for MPs and Lords to be "flouting a court order just because they disagree with a court order, or for that matter because they disagree with the law of privacy which Parliament has created".
Liberal Democrat MP John Hemming, who has recently highlighted two cases in parliament, said the judges' review of the use of injunctions was an "attempt to gag the media in discussing the proceedings in parliament" and was "a retrograde step".
But the judges insisted they were only following the laws as set down by Parliament, who were aware of the consequences of the Human Rights Act 1998 and the European Convention on Human Rights.
Lord Neuberger, the Master of the Rolls and the most senior civil judge, also admitted that bloggers and users of social network sites such as Twitter would not necessarily be stopped by injunctions.
The internet had "by no means the same degree of intrusion into privacy as the story being emblazoned on the front pages of newspapers", which "people trust more", he said.