Villas-Boas was sacked on Sunday, a day after his side suffered a 1-0 defeat to West Bromwich Albion. The loss was the latest in a string of league defeats that has left Chelsea off the pace in the race for a Champions League spot next season.
Pep Guardiola, Jose Mourinho and Rafael Benitez are among the favourites to succeed the 34-year-old Portuguese, though Redknapp has also been linked with the job.
But Redknapp, who is tipped to become the next England manager, admits that while the post at Stamford Bridge is an attractive one, he is not interested in a move to Tottenham's cross city rivals.
"It would be difficult. I wouldn't be able to come back to north London," he said. "So no, I will pass on that one."
Despite Roman Abramovich firing six managers since taking over in 2003, Redknapp believes the Chelsea job is one of the most appealing in world football.
It's a club you can win a championship at because the owner has spared no expense," Redknapp said.
"He has built the most incredible training ground, and they buy top-level players.
"They have top players so it's a dream job for someone to go there and make a success of it, whoever they take.
"So many people would love that job and the chance to work at a great club with the backing that the manager gets there."
Redknapp said he was sad to see Villas-Boas lose his job after just eight months, but conceded that Abramovich has every right to make a change.
"He owns it, he pays massive wages to the managers and if he doesn't get the success he wants then he is in a position where he is not going to sit back and do nothing," Redknapp added.
"Those are the rules you have to work under.
"When you go there you have to be successful. If not you are not, you're not going to last. That's how it works."
Redknapp thinks Mourinho, who won five trophies during a three-year spell at Chelsea, could return to Stamford Bridge, although luring the 49-year-old from his current employers Real Madrid may be difficult.
"He was fantastic when he was here in England," Redknapp said.
"He is a character. He was great at his job. There was no doubt about that.
"He beat Barcelona on the way to winning the Champions League and he is now at Real Madrid.
"He is a great personality and you just wonder if he would come back here…it would be difficult to leave a club like Real Madrid, that's for sure, but who knows, Chelsea could be the one club who could tempt him."
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