The Argentinean striker, who has 19 goals to his name this season, handed in a transfer request on Thursday, disrupting United's planning for Sunday's FA Cup fourth-round tie at home to Tottenham.
Becchio's request to move on comes amid three bids for him from overseas clubs, one believed to be in China, and towards the end of a month which has seen Warnock criticise the player for allowing his head to be turned by talk of a move away.
The 29-year-old has 18 months left to run on his current deal and Warnock claimed that they have offered him a new three-and-a-half-year one on the best terms he has known since moving to the club in February last year.
"It's been below the surface for a while now. We have been talking about a new contract for Luciano but it's the player's prerogative," Warnock said. "We had two offers which we turned down and another yesterday (Thursday). They're all from abroad."
Press Association Sport understands it is Becchio's preference to remain at Elland Road, but this is not the first time Leeds' fans have seen their leading player go through a transfer saga. In recent windows, Jermaine Beckford, Max Gradel, Jonny Howson and Robert Snodgrass have all moved on.
Warnock, though, is keen to stress that Becchio is looking at things from a financial point of view rather than an ambition one.
"I've had a chat with him and what we said remains private," he said.
"He was a late starter in professional football and he feels at the moment, that the opportunities he will get abroad, and the type of figures he's been given, he will have security for life.
"He is thinking about his family and his life. We have offered him three and a half years, on more than anyone I've known since I've been here, but that was not acceptable to his advisors."
- Sports & Recreation