The Portugal international is set to become a free agent this summer after failing to earn a new deal to extend a 10-year stint at Santiago Bernabeu.
Hamann, though, believes that his experience and quality could be put to good use at Anfield, with Jurgen Klopp needing to add depth to his squad ahead of a return to Champions League competition.
I'd take Pepe to @LFC in a heartbeat— Didi Hamann (@DietmarHamann) June 21, 2017
Former Liverpool midfielder Hamann saw his initial suggestion questioned on Twitter, but the German was quick to point out that Pepe’s class has been proven over several years at Madrid and as a European Championship winner with Portugal.
Look what he's won my friend.If he was that rash he wouldn't have played for biggest club in the world that long.He's a winner and is class https://t.co/W0upecmwfo— Didi Hamann (@DietmarHamann) June 21, 2017
Hamann also believes that Pepe could make a similar impact at Anfield to that of Luis Suarez, with both men enigmatic characters who boast the ability to excite and frustrate in equal measure.
We had a Uruguayan forward a few years ago https://t.co/GenqPghayu— Didi Hamann (@DietmarHamann) June 21, 2017
Pepe is currently away on international duty at the Confederations Cup and has made it clear that no decision on his future will be taken until Portugal’s involvement in that competition comes to a close.
He told reporters when quizzed on the issue: "My future is the national team.
"I don't have a contract at the moment, but I just want to make the most of the national team and the chance to succeed in the Confederations Cup.”