The Mirror says Liverpool had appeared in pole position for his signature when managing director Ian Ayre jetted to Catalunya for talks over a move in November.
However, the player's future remains unresolved and though contract talks with Los Cules have broken down, Liverpool face a transfer scramble to bring the right-back to Anfield.
According to Josep Maria Orobitg, Montoya's agent, a number of clubs are keeping tabs on the Spanish under-21 international.
"At the moment everything is stopped [regarding a renewal with Barcelona]," said Orobitg, speaking to Tutto Mercato.
"The situation is clear - if we cannot reach an agreement on a new contract, Montoya will be free to find a new club. It's a complicated situation.
"Possible future in Italy for Montoya? Every day I have to clarify the situation of Martin, who has been requested by three clubs in Serie A.
"Montoya also has enquiries from other major European leagues, not just Serie A."
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