Milner’s current contract with City runs out at the end of the season, and no new deal is in place.
According to The Daily Mail, both Arsenal and Liverpool are interested in the England international.
Former Liverpool midfielder Redknapp seems to be a fan of the former Leeds United and Newcastle United star, and believes that he could end up at Anfield next season.
“It's ridiculous that James Milner is 90 minutes away from being a free agent,” the 41-year-old wrote in The Daily Mail. “He is such a good all-rounder, as his stats show, and helps Man City’s homegrown quota.
“But he wants to play. I wouldn’t be surprised if he ends up at Liverpool in a high-energy midfield with Jordan Henderson.”
Milner has been on the books of City since 2010, but he has never really been guaranteed a regular place in the starting line-up.
The former Aston Villa star has scored five goals and created 49 chances in 31 Premier League appearances this season, while having a pass accuracy of 80% and a shot accuracy of 41%.
The Englishman is not one of the most technically gifted footballers, but he is an all-round midfield player who works hard and does what he is told.
Given the fact that Milner has loads of Premier League experience and would not cost any transfer fee, it would be a good piece of business for Liverpool if they recruit him.
However, even at Liverpool, who will be challenging for a top-four finish in the Premier League next season, there will not be any assurance that Milner will get to play every week.