Following a meeting with manager Rafa Benitez, it's become clear the German's chances of first team football would be limited this season.
Hamann triggered a one-year extension to his Liverpool deal during the course of the last campaign, and originally intended to remain on Merseyside.
But the emergence of Momo Sissoko, and return of Steven Gerrard to his favoured central midfield role next season, means Hamann will have fewer opportunities to feature.
His departure would bring an end to a hugely successful Anfield career, during which time Hamann won every major honour apart from the Premiership.
After signing for £7m from Newcastle in 1999, he was a key member of the cup treble winning side of 2001, and more famously helped transformthe Champions League final as a second half substitute.