QPR manager Harry Redknapp, meanwhile, is trying to persuade club chairman Tony Fernandes to agree on a deal to bring the 32-year-old Defoe into the fold in January, according to the Daily Telegraph.
The Daily Mail says Toronto is willing to let Defoe go for the right price, but wants a permanent deal rather than a loan.
That could be a stumbling point.
"You never know, do you? It's a difficult one, because of the whole package," Redknapp said when asked about Defoe at his news conference before Friday's game with Arsenal. "Really we're looking for loans, we're not looking to spend money in the (transfer) window.
"We're looking to bring a couple of loan (players) in if we can, some good loans. That's where we're at ... We're not looking to be spending big money in the transfer window."
Redknapp is reportedly keen to sign a striker to help forward Charlie Austin.
The Telegraph says Redknapp, who managed Defoe at West Ham, Tottenham and Portsmouth, believes Defoe can help the club avoid relegation. QPR stands 16th in the table with a 5-10-2 record.
Toronto turned down a club-record transfer bid for Defoe in the summer.