Forest boss Billy Davies is keen to bring the prolific Argentine to the City Ground in January and is prepared to part with £1million for his services.
Becchio, who has been a consistent scorer in the Championship and League One in recent seasons, is yet to sign a new Leeds contract and Davies sees him as a perfect replacement for the injured Dexter Blackstock.
The Forest boss confirmed he will attempt to bring in some quality in the transfer window to help the ninth-placed club move into the top six and subsequent promotion play-offs.
"The next window is very important and I want us to get new players in January as early as possible," he said.
"Over the next few weeks I will be presenting my list of players to David Pleat and the transfer acquisitions committee and that is all we should be focusing on."