The Scotsman has been at the helm of the Toffees since 2002 with some calling for him to move on after more than a decade.
But Republic of Ireland right-back Baines Coleman feels that Moyes has achieved enough at Everton to choose his own fate.
"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 at the club."