The 23-year-old French international is in the final 12 months of his contract, and has attracted attention from a host of foreign clubs, with his freedom to negotiate a pre-contract agreement as soon as January.
Gunners boss Arsene Wenger has been linked with Yanga-Mbiwa for over a year, and was believed to be considering a cut-price bid to bring him to the Emirates Stadium when the transfer window reopens in the New Year.
However, Arsenal expected competition from Serie A giants AC Milan, who have also been monitoring the defender's situation.
But, with Montpellier now ready to hand Yanga-Mbiwa a new two-year contract, a switch to England or Italy now seems increasingly unlikely.
It's understood the Ligue 1 club will also increase the minimum fee release clause written into the player's contract, to strengthen their bargaining position, in the hope it will spark a bidding war between Arsenal and Milan next summer.