New Queens Park Rangers manager Redknapp has been linked with a move for the England striker, who he worked with at Spurs, West Ham and Portsmouth, as he looks to save the Premier League's bottom side from relegation.
Redknapp led the Hoops to a 0-0 draw at Sunderland in his first game in charge on Tuesday, but his new charges remain eight points adrift of safety.
Rangers are the lowest scorers in the top-flight, after managing just 10 goals in their opening 14 matches, with Redknapp knowing he needs more firepower at his disposal.
But Villas-Boas insists 10-goal Defoe, often overlooked by Redknapp at White Hart Lane last season, will not be leaving.
"That's not possible," Villas-Boas said when asked about the prospect of Defoe leaving in January.
"It's absolutely impossible. We have the belief in him."
Villas-Boas admits Defoe is among the best strikers he has worked with and even ranked him alongside Colombian striker Radamel Falcao, who scored bags of goals for the Portuguese boss at FC Porto and is now setting the Spanish league alight with Atletico Madrid.
"I certainly put him alongside Falcao," added Villas-Boas.
"His hunger for goal is extreme. That makes things easier for you to work with because you don't have to teach a lot.
"He smells every cross and when the opportunity is there to tap it in."
However, Villas-Boas has refused to rule out the prospect of defender Michael Dawson linking up with Redknapp again.
"I think if that possibility arises we will have to consider it," he said.
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