The AC Milan midfielder was approached by several clubs, including the Gunners, but is happy at San Siro and would be hard to prise away despite the team's poor season
The Gunners were in the market for midfield cover during the January transfer window, with Kim Kallstrom drafted in from Spartak Moscow after Aaron Ramsey's recovery stalled – though the Swede has yet to play for the north Londoners due to a back injury.
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"Milan have had a difficult season so far and I think I can say that Riccardo Montolivo has been one of the brightest notes,” Branchini told Calciomercato.
"He became a fixture of the Rossoneri and was even given the captain's armband as proof. He is very happy with the club to which he belongs, and the club and fans are very satisfied with him.
"An extension? He has a contract until June 2016, so it is not a priority to talk about an extension at this time. That's a discussion we'll have, I think, next year.
"Has there been interest from other clubs? There have been tentative enquiries from Atletico Madrid, [Dortmund boss Jurgen] Klopp and Arsenal, to name a few.
"All were trying to ascertain whether the 'path' to Montolivo was feasible. At the moment, however, I feel it would be very difficult for the player to leave Milan, precisely because of what I said before."