The Serie B side, who are also interested in Leeds striker Mirco Antenucci, have negotiated a deal to sign Bianchi until the end of the season with a view to a permanent move.
Bianchi is out of favour at Leeds and has not made a first-team appearance since undergoing surgery on a knee injury last season.
The 27-year-old required a second operation in August and has been limited to outings for the Under-21s this term.
Steve Evans left him out of today’s development-squad game against Barnsley following Ascoli’s approach for him.
Evans said: “He’s got permission to speak to them and that’s likely to happen.
“He’s a fantastic lad and he’s had a difficult time with injury but I do think the game in Italy suits him better than the game in England.
“It would be a good move for him at this stage and he was buzzing when I told him about it. It suits all parties.”
Bianchi signed a three-year deal with United when he joined from Sassuolo in July 2014, one of numerous transfers completed in the aftermath of Massimo Cellino’s takeover of Leeds.
He started 24 games last season but was injured during a 2-0 win at Reading in February.
Ascoli’s squad already includes former United loanees Zan Benedicic and Dario Del Fabro but their attempts to land Antenucci have so far failed.
The striker is nearing the last six months of his contract at Elland Road and is understood to be keen to secure a move to Italy following the birth of his second child last week.
Leeds, however, are already short of forwards and their reluctance to lose Antenucci in this transfer window appears to be pricing Ascoli out of a deal.