With his deal running down this season, the midfielder is attracting interest from Newcastle United.
Wyness told Football Insider's podcast: “I think there’ll be interest. I think right now he’s getting his contract renegotiated.
“But look, Garner has always had a lot of interest. When he left Man United and went on loan to Forest, he was very well thought of there.
“He’s a good player. He’s a very good, honest, decent Premier League player.
“He’s done a lot for David Moyes in terms of versatility and I know that Moyes really rates him, really likes him, and I think James is happy there. His contract will get resolved.
“He’ll be part of the squad going forward. I think everybody knows that James is going to get what he wants anyway. So, I expect him to be longer term at Everton, no problem at all.”