Reports suggest the 30-year-old midfielder could be heading to the Madejski Stadium on a season-long loan.
Cole spent last season on loan at French club Lille and Liverpool may be open to a similar deal again.
Cole joined The Reds on 2010 but lost his place in the side under Kenny Dalglish.
However, Dalglish was sacked earlier this week which could pave the way for Cole's return under the new boss.
Ex-Reading boss and current Swansea City manager Brendan Rodgers turned down an invitation today to talk to Liverpool over the vacant hotseat. Barcelona's Pep Guardiola and Wigan's Roberto Martinez are other possible contenders to succeed Kop hero Dalglish.
But Cole's wages - said to be £70,000 per week - could me a major stumbling block in any possible move to the Royals.
Meanwhile, Reading boss Brian McDermott made his first summer signing this week with the capture of Garath McCleary from Nottingham Forest on a free transfer.
The tricky 25-year-old winger signed a three-year contract at Madejski Stadium after rejecting a number of rival clubs including West Bromwich Albion.
** READING will host Crystal Palace in a pre-season friendly at Madejski Stadium on Saturday, August 11 (3pm).
Royals drew 2-2 with Dougie Freedman's side in the final home fixture of last season on the day they clinched the Championship title.
Brian McDermott's side also face friendlies at AFC Wimbledon (July 14) and Salisbury City (July 28) and will play three games on pre-season tour to Portugal between July 19-28 **