The Reds have chased the Spaniard for much of the last few years, but their pursuit appeared to have ended in disappointment when he penned a new contract with the Catalans not long ago.
However, new Barca boss Luis Enrique is understood to have deemed the 23-year-old surplus to requirements this term, after handing him just one outing so far.
Montoya himself is desperate to play, which has opened up the possibility of a January loan or permanent transfer.
Liverpool are expected to be interested, with Brendan Rodgers plotting for life beyond Glen Johnson – who is unlikely to see his deal, which expires at the end of the current campaign, extended.
Montoya is a product of Barcelona’s famed academy set-up and has made 38 first-team appearances, winning two La Liga titles – albeit with a minimal role.
Inter Milan are also keen, but it’s understood that the defender would prefer a Premier League switch.