The Reds were thought to be in pole position to sign the Spaniard, after managing director Ian Ayre flew out to Spain for talks in November.
The 22-year-old is out of contract at the Nou Camp in the summer, and had been heavily linked with a January move to Anfield.
However, Liverpool have been unable to reach an agreement for the Spanish starlet, despite the fact he is yet to sign a contract extension with Barca.
Talks between Montoya and Liverpool chiefs appear to have stalled, and reports in Spain suggest he is ready to commit his future to Barcelona by signing a new long term contract.
The La Liga giants remain keen to keep hold of one of their homegrown talents, and could finalise the new deal as early as this week.
The news will come as a blow to Liverpool boss Brendan Rodgers, who had identified the Spaniard as a top transfer target for this month.
Montoya has played 12 games for Barcelona this season.