Sagna is only now returning to action after a lengthy spell on the sidelines, but only has 18 months left on his current deal and talks do no appear to be taking place right now.
That has put the Serie A outfit on red alert as they are apparently a big admirer of the Frenchman and would love to bring him to the San Siro.
Inter look like making a serious challenge for the league title this campaign and are ready to strengthen their squad in the New Year.
It seems as though Sagna is not overly happy with the Gunner either, after comments earlier in the season suggested he was not best pleased with Arsene Wenger selling Robin van Persie in the summer window and believes that the club should not be letting their best players go.
However, he could be the latest big name to leave the Emirates, especially with 20-year-old Carl Jenkinson currently impressing and keeping Sagna out of the side.
Inter seem confident that they can land the full-back in January with a decent offer.