The Spaniard was linked with the Premier League duo over the summer, but eventually opted to stay at the Nou Camp, where he was expected to pen a new deal.
However, negotiations have since moved slowly, leaving the door ajar for a free transfer at the end of the season.
Montoya is said to be seeking assurances over his future at the club, and is growing increasingly frustrated at having his path into the first-team blocked by Brazilian superstar Daniel Alves.
Although the 22-year-old is fully committed to Barca in the short-term, his agent, Jose Maria Orobitg, has revealed that he could opt to leave the Catalan giants once his contract expires.
“For the moment he is under contract with FC Barcelona until the end of the season,” he told The Express.
“However, the contract extension has still not arrived.
“We have talked but there is no certainty that Martin Montoya would hold down a first-team spot, because right now Daniel Alves closes the door.
“The transfer window is closed, but I can tell you that the contract extension may not be successful.
“Anything could happen between now and June.”
Montoya is a graduate of Barca’s much-praised La Masia youitha academy, and has made 36 appearances for the club’s first-team.
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