The Premier League club have reportedly held talks with their former defender as they look for a successor to Ian Holloway and bookmakers have made him favourite for the job.
Relations between Coleman and the FAW have been strained after some disappointing results brought failure in World Cup qualifying.
The former Fulham manager is also said to be keen on the idea of a return to the Premier League with his contract set to expire next month and his Wales future uncertain.
Tony Pulis was the frontrunner to take charge at Palace after Holloway left the club last week, but the lack of progress has led to others entering the frame.
Meanwhile, Palace captain Mile Jedinak says he is confident the club's hierarchy will make the right decision when they come to make an appointment.
Keith Millen, promoted from assistant boss to caretaker, has taken charge for the last two games. Defeats to Arsenal and West Brom have extended the Eagles' Premier League losing streak to seven matches.
After the Albion game, Millen, who is not applying for the job, made it clear that while he did not know when a new boss would be confirmed, as far as he was concerned the sooner it happened the better.
And asked for his thoughts on the situation, Australia midfielder Jedinak said: "We are in good hands and I am sure the powers that be will make the right decision."
He added: "We understand that it is a big decision and these things may take time.
"Whatever the club decide to do, we support that. We as a group have to stick together as we have been doing."
Holloway indicated on his departure that he felt he did not have the necessary energy to keep Palace up, but Jedinak - who is in talks over a new contract with the Eagles and hopes to sign it soon - thinks the club are far from a lost cause this term.
He said: "It is a big opportunity (for the new manager). You have seen enough the last two weeks to know that it is definitely something worth fighting for. We are not going to give up."