The 22-year-old, whose current deal expires next summer, has been linked with a number of European clubs over the last few months.
"For the moment he is under contract with Barcelona until the end of the season. However, the contract extension has still not arrived," Jose Maria Orobitg told Sky Italia.
"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.
"In the past, Inter Milan, Napoli, Bayer Leverkusen, Dortmund and Liverpool were interested. Anything could happen between now and June."
Arsenal are the latest club to be linked with a move for the right-back.