Just six weeks ago the player said he would not play for the Gunners "for £200,000 a week" after he was fined £100,000 (€145,530) at a Premier League inquiry for meeting Chelsea boss Jose Mourinho and chief executive Peter Kenyon.
But the left-back's agent, Jonathan Barnett, revealed that Cole is expecting to agree a new deal with the Highbury club soon.
"I am pleased to say amicable discussions have taken place in the aftermath of a very difficult situation.
"Both sides are now close to an agreement that would see Ashley remain at Highbury.
"Perhaps now people will believe there were no secret deals to join another club."
The Premier League acted following newspaper reports in January that Cole, Mourinho and Kenyon met at the Royal Park Hotel at Lancaster Gate, London.
Chelsea and Mourinho were
condemned for "blatantly disregarding" Premier League rules, while Cole's position at Arsenal was not helped by the fine he received for making an illegal approach to the Blues.
An independent panel is set to hear the defender's appeal against his punishment after the Arsenal full-back was found to be in breach of Premier League Rule K5, which governs approaches by contracted players to clubs.
But Gunners boss Arsene Wenger insisted he wanted Cole to remain at Arsenal and the news will lift the club following this week's €19.9 million departure of captain Patrick Vieira Juventus.