The current deals of veteran striker Emile Heskey, defender Carlos Cuellar and number two keeper Brad Guzan run out in June.
Villa have held initial negotiations with Cuellar and Guzan with the former already indicating he would like to remain at the midlands club. But Grant said: "The gaffer (Alex McLeish) has said he would rather put all these talks back until the season ends."
He added: "Alex has always been one of those guys who prefers to do his business at the end of the season.
"He knows the most important thing is Villa winning games.
"His thinking is 'I'd rather leave it as much as I possibly can' and I think the players we are working with understand that."
Cuellar has been in outstanding form since being restored to the side and Guzan showed his potential during a two-month run in the side when Shay Given was injured.
But Heskey is no longer a first-choice striker although he was restored to the side for last weekend's clash with Arsenal.
Source: PA
Source: PA