The QPR boss has moved to gazump Sunderland's bid to take Borini back to the Stadium of Light on loan or on a permanent basis, with Liverpool accepting Rangers' initial £10million offer, Press Association Sport understands.
Black Cats boss Gus Poyet admitted he could not reveal all the details surrounding Sunderland's protracted negotiations over a season-long loan with Borini on Saturday, and now QPR are ready to beat the Stadium of Light outfit to the punch.
Italy striker Borini spent last term on loan with Sunderland, notching seven goals in a productive spell and leaving Poyet keen to secure the 23-year-old's services on a repeat temporary deal.
Former Uruguay midfielder Poyet said after Sunderland's 1-0 loss at QPR on Saturday that he remained hopeful of securing a deal for Borini before Monday night's transfer deadline.
"I know how people feel but unfortunately we cannot give you all the information, all the true information on why he's not with us," he said.
"I know from the outside it looks like it's him not wanting to come to Sunderland because of whatever, but I can promise you it's not like that."
Rangers boss Redknapp has moved in with an offer for a permanent transfer that Liverpool have accepted, with a fee that could rise to £13million with add-on clauses.
Former Tottenham boss Redknapp remains hopeful of completing a deal to bring midfielder Sandro to Loftus Road from Spurs, while Jermain Defoe has been heavily linked with joining QPR from Toronto.
Lassana Diarra's proposed transfer has fallen through, however, despite the midfielder passing a medical on Saturday.
Diarra watched Rangers' victory against Sunderland from the Loftus Road stands, with Redknapp saying the deal was complete barring paperwork.
However, the Lokomotiv Moscow midfielder's move has now fallen apart, denying Redknapp the chance to work with the France midfielder he signed at Portsmouth.