And Moyes, who played with Beckham at Preston when the midfielder was 19, is hopeful he may fancy another loan move.
He said: "I hope that if David wanted to come he would give me a call. He only needs to call me or Phil Neville."
Beckham and Everton captain Neville are friends from their Manchester United days where they came through the ranks as juniors.
And Moyes added: "He knows how to get hold of Phil and he knows how to get hold of me.
"We would have to look into it financially. But if he came and said to me 'I would like to come and play' then I would have to go to the chairman and ask if we could make it work by selling enough replica shirts."
More to follow.