The 29-year-old Argentinian striker still has 18 months left on his current contract, but has been linked with a move to Wigan, although Latics boss Roberto Martinez recently played down suggestions a transfer was imminent.
Warnock revealed after last Saturday's 2-0 loss at Barnsley that the player's "head was being turned".
"I've spoken to him but there's only so much you can say," said Warnock. "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.
"Once the deadline's gone I'm not bothered because he'll get down to it and be back to normal. It's just that the heads get turned and you can't stop that. It's a nightmare scenario."
Becchio is enjoying a prolific season in front of goal, having scored 19 times in all competitions.