The 29-year-old, who joined the club from Chelsea last July, has made only eight starts in his debut season at Anfield and has lost his place in Fabio Capello’s England squad following a stuttering campaign.
With a busy summer in the transfer window expected on Merseyside, Cole would command a fee of £10 million and both Tottenham and former club West Ham are thought to be interested in the playmaker.
However, Cole’s £100,000-a-week contract would possibly be a stumbling block for any potential suitors, with the midfielder's form dipping off dramatically after an impressive spell at Stamford Bridge.
The Sun quotes a Liverpool insider as saying: "It's tough on Joe because he is a great kid. But things just haven't worked out for him.
"Kenny is building a new Liverpool with the likes of Andy Carroll and Luis Suarez and he wants to bring in more new players in the summer.
"And, unfortunately, that means Joe will be surplus to requirements."