Jurgen Klopp’s Liverpool reclaimed top spot in the Premier League after their emphatic 4-0 win at Bournemouth in Saturday’s early kick-off.
Mohamed Salah netted a hat-trick, while Steve Cook scored an own goal for the hosts.
City now need at least a point at Chelsea in the evening game to go back to the top of the table.
And the former Reds midfielder says Klopp’s side can push City all the way both at home and in Europe.
“They’re purring right now,” Redknapp said.
“And if they can get through on Tuesday (in the Champions League against Napoli]), keep going in the Premier League, they can hang onto Man City’s coat-tails.”
Liverpool kept yet another clean sheet – their tenth in the top flight already this season.
Virgil van Dijk was a rock at the back once more, while Salah flourished in his new role as the central striker.
And Redknapp believes the prolific Egyptian is now playing in his best position.
“Virgil van Dijk can wear his kit (that he wore against Bournemouth) on Tuesday night, it was that clean,” he added.
“Liverpool never got out of second gear, it was so comfortable in possession.
“When you’ve got a player like Salah, he can take a game away from any team.
“The problems he causes defenders, running on the shoulder, the third goal epitomised that.
“I thought Liverpool were very comfortable and it shows the strength of the squad they have.”