The Irish international said the Scot has earned the right to choose whether to remain on Merseyside in his own time, but added that he hopes the Blues boss stays put after his contract expires this summer.
"The manager's situation is his own situation and he has been around long enough to earn the right to decide what he wants to do," Coleman told Sky Sports News.
"Obviously we would all love him to stay but that is up to him and we have just got to keep playing as well as we can and try and finish as high in the league as we can.
"Personally speaking he has been great for me, since I came in, he has always been there to tell me what I am doing well, what I have done wrong and a manager of his experience you are going to listen and you can see why he has been so successful a the club."
Everton currently occupy sixth place in the Premier League, two points away from Tottenham Hotspur above them, although the London club have a game in hand.