Hamann believes Cole would be the ideal signing to strengthen the left-back position for Liverpool, with the area in urgent need of improvement his summer.
On-loan defender Aly Cissokho is set to return to Valencia in the next few weeks while Jose Enrique has battled injury problems this season. As a result, Jon Flanagan has been forced to deputise in the position - although he has done a fantastic job.
But Rodgers is still expected to target another full-back during the summer window, and with Ashley Cole out of contract at Chelsea, Hamann believes he could be the perfect acquisition.
"Cole hasn't played a lot of football this season but I watched him against Liverpool and against Atletico Madrid and he was absolutely outstanding," Hamann told talkSPORT.
"The guy has still got it. If I was Liverpool or Tottenham I would do my utmost to get him for a year or two because he has that left in him and he's still a top, top player."
Liverpool finished second to Manchester City in the Premier League this season, and their defensive fragilities cost them dearly. They conceded 50 goals over the course of the campaign, a figure closer to the bottom half of the table than the top.
Cole missed out on a place in Roy Hodgson's World Cup squad, and the Chelsea defender has decided to retire from international football. Liverpool's Flanagan is on the stand-by list.