The 23-year-old Belgium international has become a cult figure at Goodison Park since arriving from Standard Liege three years ago, but he has been linked with a host of leading European clubs.
Moyes, though, is hopeful of keeping him on Merseyside, saying: "I think talks have started now, even though I`ve not spoken to Marouane personally about it.
"He's really important to us, part of the furniture here now, and of course we want him to stay.
"We did it with the likes of (Phil) Jagielka and (Leighton) Baines who are on long-term contracts. We want to keep building on that and obviously Marouane comes into that category.
"In the main, the chairman has done a really good job keeping hold of players, so we`ll see how we go with Marouane, too."
Source: PA
Source: PA