Glen Johnson currently earns a reported £120 000-a-week at the Reds but will not be offered a new deal which matches his current deal according to the Daily Mirror.
With Johnson set to depart the club at the end of June, Brendan Rodgers has sent his scouts on a mission to find a new right back.
Reports in England suggest that AC Milan defender Ignazio Abate is Liverpool's first choice target.
Abate has so far failed to agree a new deal with Milan and will be allowed to join Liverpool on a free on July 1.
Liverpool will be monitoring the Italian's contract negotiations with a keen eye and may yet decide to make a January move in order to avoid losing out on the 27-year-old.
Joel Ward is also being linked with Liverpool but the defender has a new offer from Crystal Palace, who want to keep the young defender at the club.
Crystal Palace manager Neil Warnock confirmed that the club have been in discussions with Ward over a new deal.
"I think that Joel is an important player." said Warnock.
"It doesn’t mean that he will sign a contract. He’s got his options, speaking to the lad himself.
"I think it’s important that the club make offers like this to players, not just when their contract has expired, but in plenty of time when you value their service."