Becchio handed in a transfer request earlier this week and is keen to find a new club, but Leeds have not given up hope of keeping their top scorer.
Warnock concedes that the situation is far from ideal but does not rule out starting Becchio when Leeds host Tottenham Hotspur in the FA Cup on Sunday afternoon.
He said: "I shall see how Luciano looks in training and make sure his head's right in the next 24 hours before deciding whether to chuck him in against Spurs. If I'm honest, I have to say his mind has not been on his business over the last few weeks.
"But he is a good pro who always gives 100% on the pitch and I expect that to continue for as long as he remains at this club. I am not pleased about this situation with Luciano.
"You can never be happy when offers come in for your best players. We have tried to settle Luciano down by holding talks over a new deal for him. We have put a Premier League-size contract on the table, certainly the biggest I have known in my time as manager here, but he just doesn't want to know."