The Argentinian striker handed in a transfer request on Thursday after the club rejected two bids for him this month.
Leeds have already tabled a new three-and-a-half-year deal for Becchio but Warnock stated that the club's new owners GFH Capital will not increase the offer.
"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," ITV Sport quotes Warnock as saying.
"We had two offers which we turned down and another yesterday. They're all from abroad.
"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."
Becchio has scored 19 goals for Leeds this season.