Redknapp wants to keep Nelsen playing — and helping the London side climb out of the Premier League relegation zone.
Nelsen is under contact with QPR through June 30. The MLS season kicks off March 2, with training camp slated to open later this month.
The Guardian newspaper reports that Redknapp wants to hang onto to Nelsen until his team's fate is decided. QPR (2-12-7) is currently last in the Premier League standings.
The 35-year-old Nelsen has been one of QPR's most effective defenders this season. He has made 18 league appearances, most recently playing 71 minutes in last Saturday's 1-1 tie with West Bromwich Albion.
QPR play Tottenham, Redknapp's former club, this weekend.
Toronto FC unveiled Nelsen as its new manager on Tuesday at BMO Field, acknowledging it was unsure when he would be free of his QPR obligations. Toronto president and GM Kevin Payne said he was willing to wait with newly appointed assistant coach Fran O'Leary on standby to lead the team in Nelsen's absence.
Toronto season ticket-holders, meanwhile, got an email from Nelsen on Thursday about his plans for the struggling MLS team.
"Going forward our team will match the passion and dedication of our fans each and every day," the New Zealander said. "TFC will become a fiercely competitive team and BMO Field will be one of the most difficult places to play in the league. TFC will never give up. This is how our team will be built."
"I'd like to thank you for your continued support of Toronto FC," he added. "The Red Thread binds us together, and together we will be successful."
Adding to Redknapp's problems is that QPR has been rebuffed in a five-million-pound bid for West Brom's Swedish defender Jonas Olsson.
"A bid came in from QPR for Jonas," West Brom manager Steve Clarke is quoted on the club website.
"We turned it down flat and we don't encourage anymore bids because he's not for sale."
Redknapp is reportedly also interested in veteran Spurs defender William Gallas.