The Whites' in-form forward has netted 19 goals in 29 appearances this season, with such a healthy return drawing inevitable interest from afar.
A step up to the Premier League has been touted, with the market having re-opened for business.
Leeds are aware that they have sought-after talent on their hands, with promising defender Sam Byram also generating plenty of speculation, but Jones hopes they can make it to 1st February with their squad intact.
He said: "My biggest fear is that there could be pressure on us from other clubs for him (Becchio).
"Look at his form at the moment and he's bound to be hot property. I'd be worried if certain clubs came in for him both here and abroad."
Jones added: "We're working hard to keep him and Sam Byram beyond the end of their current contracts.
"I don't think Sam will go because he's in the right place to develop as a player but there might be some pressure to sell him."