The highly rated player is known to be available for around £6m, but he is also not keen to leave London just yet.
"Scott Parker would certainly be a name we'd be interested in," said Moyes. "I expect good players to be attracted to Everton because we are clearly moving in the right direction. They will see us making good progress and they will be aware of this club's history. When you know a club has been there and done it, it does make it more attractive."