The Reds have already had a bid rejected for the 23-year-old stopper, but they are not giving up on the talented defender.
Pearce has just over six months left on his deal at Madejski Stadium, meaning he will be available at a cut-back price in January.
Daily Mail suggests that the Ireland Republic international is unhappy with the contract terms offered by the Royals, which is why he was dropped from the starting line-up by boss Brian McDermott.
Pearce was voted Reading’s Player of the Season last term and started first four Premier League games for the Royals this season, but was then relegated to the bench as a punishment for not agreeing a new deal at the club.
Liverpool boss Brendan Rodgers has a very high opinion of the stopper and will attempt to lure the player to Anfield in January.