"We have a good relationship," Moyes said of Gravesen. "What the outcome will be, I don't know yet. Tommy wants to play in Europe and we are not in a bad position to help him get that.
"He's really well liked here and it's not always the best thing to move. He wants to see that we're going to make progress as well and hopefully we'll be able to show that in the coming months.
"We think this is going to be a good club to be at in the future. We have a number of players in the last year of their contracts, but they have a real chance of staying - given how well they have performed."
Rumours have been circulating recently that Man Utd were after Gravesen in January, with Phil Neville, John O'Shea and Kleberson all being linked with a swap deal.