The married star, who is referred to as CTB in court documents, is said to have had a “sexual relationship” with the former reality television contestant.
He obtained an order preventing The Sun newspaper from revealing his identity last month and has now filed a lawsuit against the micro-blogging site and “persons unknown”.
The legal action is thought to be the first of its kind against Twitter.
Lawyer Mark Stephens, who does not represent anybody involved in the case, said documents were filed at London’s High Court on Wednesday.
While the player could win his case against the “persons unknown”, he is unlikely to succeed against Twitter which does not fall within British jurisdiction, Stephens said.
“If you want to sue Twitter, you have to go to San Francisco,” he added, referring to the company’s headquarters in the US.
“I think it (this action) is manifestly ill-conceived because Twitter is not within the jurisdiction of England and Wales and he (the footballer) will have to launch proceedings in California which would be snuffed out like a candle by lawyers for Twitter.
The legal bid comes after a Twitter user identified a number of individuals who were said to have taken out gagging orders, fuelling the privacy debate and highlighting the problems associated with enforcing injunctions.
The list of celebrities has reportedly been seen by two million people.
A Twitter spokesman said: “We are unable to comment”. Lawyers at Schillings, who represent CTB, have yet to respond.
It came as the most senior judges in England and Wales have been accused of trying to gag the media after criticising politicians who have deliberately disclosed the content of privacy cases covered by injunctions.
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”.
Lord Neuberger, the Master of the Rolls and the most senior civil judge, also warned that reports of comments which intentionally contravene court orders may not be protected by parliamentary privilege.