Coleman's current contract comes to an end after next week's game against Finland and so a possible new deal will be up for discussion.
He was due to name his squad for the Finland game at a news conference on Friday but it has been cancelled because the FAW felt it would be dominated by questions about Coleman's future.
Coleman has won four of his 14 matches since taking the Wales job, with a pair of draws and eight losses.
And he is currently odds-on favourite with the bookmakers to succeed Ian Holloway as manager at his former club Crystal Palace.
Regarding the cancellation of today's press conference, an FAW spokesman said earlier in the week: "We have discussed it with Chris and we have decided to release the squad by email, because it would be a worthless exercise holding a press conference when all the questions will be about Chris' contract and Crystal Palace.
"We are not hiding anything. Chris will be in Cardiff on Friday."
Wales only finished fifth in their World Cup qualifying group but they ended with a win over Macedonia and a creditable draw against group winners Belgium.
Speaking after the Belgium game, Coleman said: "If I had lost these two games, I wouldn't have been expecting to have been told I wasn't the man to take us forward.
"Equally, two great results does not mean I expect to be told I am the man to take us forward.
"I'm the same manager as I was last month. I never plan differently but, ultimately, it's about results.
"My contract ends in November and we have a friendly against Finland next month and we will talk about it then."
Coleman lost his assistant coach this week when John Hartson decided to step down due to his desire to spend more time with his family and his growing media commitments.