He joined Palace in 2009 and has scored four goals in 14 games for the Championship strugglers this season. Last summer he was linked with a £750,000 move to QPR but he ended up signing a new deal with Palace.
Ambrose made his England U21 debut in 2003 and played alongside players such as Glen Johnson, James Milner and Darren Bent. He also appeared for England at the U21 European Championship finals in 2006.
However, he has dropped out of contention with England under Fabio Capello and has now turned his attention to declaring for Ireland.
Ambrose qualifies through an Irish-born grandparent. He was mentioned as a possible 'signing' for Ireland when FIFA changed the rules on international eligibility two years ago, opening the door for players to switch countries even after they had played competitively at underage level for another nation.
Players such as Jamie O'Hara, Andy Lonergan, Mark Noble, Gary Cahill, Kyle Naughton and Ambrose were mentioned as possible recruits for the Irish side.
Recently, the name of Wolves winger Adam Hamill has also popped up on the radar as a possible Irish recruit, though that would be a controversial one as the English-born player's only qualification is through a grandparent who is from Northern Ireland.
So far, Trapattoni has not called in any of the new-found Anglos, but the Herald has learned that Ambrose has been in discussions with the FAI and has begun the process of clearing the necessary paperwork with FIFA to change eligibility from England to Ireland.
"The Irish management team are dead keen on Ambrose. He's started work on the passport and the other paperwork," said a source.
West Ham player Noble is believed to have come closest to a call-up from Trapattoni as the Ireland manager is a big fan of the midfielder.
Noble was reportedly being considered for a call-up for the friendly against Norway late last year but any chance of that happening was ruled out when Noble suffered a knee injury and he has only recently returned to action.