The Argentine forward has been linked with a move away from the Championship club, with Wigan Athletic rumoured to be interested in signing the 29-year-old, but Warnock has insisted that they will do all they can to keep him in Yorkshire.
Warnock told Sky Sports News: "I've spoken to him but there's only so much you can say. No doubt we'll be speaking over the next 10 days to him or his agent.
"We want Luciano to stay and that's our prerogative and he's got 18 months left. We're not the ones turning his head so we'll have to wait and see what his head's like.
"That's the answer - on the field of play. Only the next couple of weeks will tell us."
Becchio has scored 19 goals for Leeds this season.