Liverpool have been heavily linked with a move for Thiago in recent months, and speculation over his future at Allianz Arena is beginning to intensify ahead of the new season.
Bayern are reportedly holding out for a €30 million (£27m/$36m) fee for a prized asset, who has made it clear that he would like to undertake a new challenge away from Allianz Arena.
He helped Bayern win 16 major trophies in total, including seven Bundesliga titles and the Champions League, but the club have confirmed that he is seeking a transfer after turning down the chance to sign a contract extension.
Redknapp thinks Thiago would be a valuable addition to the current Liverpool squad, with it his belief that the 2019-20 Premier League champions are still lacking a creative spark in the middle of the pitch.
"We've often spoken about how good Liverpool's midfield are, how hard-working they are, but sometimes they maybe lack that bit of finesse and that little bit of quality," the former Reds star told Sky Sports.
"Thiago would give them something completely different, he's one of the best midfield players in the world. He dictates the play, plays at his own pace.
"Sometimes, especially when you go to tough places in the Premier League, you cannot beat teams by going 100 mph all the time, you need a little bit of finesse and for someone to do things differently.
"Many years ago Liverpool had midfield players like Ronnie Whelan and Jan Molby who could just slow the game down and play at a tempo that suited them, Thiago could do that.
"We saw him in the Champions League final where he completely bossed the game, had so many touches of the ball and made the game look easy."
Redknapp added on the need for Liverpool to strengthen in the transfer window in order to maintain their recent success: "Graeme Souness always talks about Liverpool's dominance in the '80s.
"The first thing they would do after winning the league would be to sign one or two players just to freshen things up and keep everyone on their toes. Sir Alex Ferguson certainly did that as well.
"I wouldn't necessarily say Liverpool have to go all in for Thiago, you've got to be careful in the transfer market.
"But Thiago would be a really good signing for Liverpool, and one who could give everybody a bit of a lift and make sure everybody knows there will be no resting on their laurels ahead of next season."