All three players are out of contract in the summer and negotiations had already begun with Cuellar and Guzan, with the Spanish defender indicating he would like to stay at Villa.
Heskey has only started 13 games this season and the former England international is no longer a first-choice striker for the Midlands club, though he is still viewed as an important squad player.
Grant said: "The gaffer (Alex McLeish) has said he would rather put all these talks back until the season ends.
"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 excellent form since being recalled to the side in place of the injured Richard Dunne, and Guzan showed his potential during a two-month run in the side when Shay Given was injured.