The England international, who has scored ten goals in all competitions so far this season, previously played under Redknapp at West Ham, Porstmouth and Tottenham.
And, since Redknapp's appointment at Loftus Road, Defoe has been strongly linked with a reunion with his former boss as goal-shy QPR face an uphill battle to avoid relegation - but Villas'-Boas was quick to dismiss any such notion.
"That's not possible," the Tottenham manager told reporters.
"It's absolutely impossible. We have the belief in him."
|AVB PRAISES RODGERS
|11/2||Jermain Defoe is 11/2 with William Hill to open the scoring against Liverpool
However, one man who could be set to join Redknapp in West London is Tottenham captain Michael Dawson.
QPR, under former manager Mark Hughes, had a reported £7.5 million bid accepted for Dawson back in the summer, but the deal collapsed after the two parties struggled to agree personal terms.
But with Redknapp now taking up the managerial reigns the Rs could reignite their interest in the four-time England international, who has played just 150 minutes of Premier League football this season.
When quizzed about Dawson's future at White Hart Lane, Villas-Boas was more open to the idea of his captain's long term future lying elsewhere, while confirming he does not expect Tottenham to be very active in the upcoming transfer window.
"I think if that possibility arises we will have to consider it," he added.
"But we're not looking to make a lot in the January transfer window."