The 24-year-old believes the manager is correct to delay the decision on his career until the end of the season, but admits he is eager to see the Scot stay at Goodison Park
The manager's contract expires this summer, and speculation has been rife regarding the 49-year-old's next move. Moyes was hired back in 2002 from Preston North-End and has been linked with a move to both Chelsea and Manchester United.
Coleman says that Moyes has earned the right to make his decision in his own time, but admits he is desperate for the manager who gave him his league debut to stay at Goodison Park.
"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.
"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 - you can see why he has been so successful a the club."
Away from the manager's future, the Toffees still remain in the hunt for a Champions League spot, and are four points off Arsenal in fourth place. Despite a five game unbeaten run, Coleman admits they are underdogs to leapfrog the Gunners and Spurs into the Champions League slots.
"There is still a chance [to finish in the top-four], which is important - I think that is the main thing that we still have a chance with five games to go," he added.
"We are underdogs for that position, which I suppose rightly so given the resources other teams have - but at the start of the season if with five games left we knew we had a chance, then we would have taken that."