Grant, who has signed a four-year deal as successor to Gianfranco Zola, has previously said that he wants to keep the 31-year-old.
However, the former Chelsea and Portsmouth boss does not want players who are not 100 per cent dedicated, saying in the Daily Mirror: "We'll do everything to keep Upson, but West Ham fans deserve players who want to play for the club.
"I want players like that because I think we'll have a great future. It will be good for us and good for the players. Of course Matthew is one of them."