Reports yesterday from German publication Bild had suggested that both the Gunners and Premier League rivals Manchester City could be possible next destinations for Martinez in the event that he were to leave the Allianz Arena this summer.
25-year-old Martinez - a senior Spanish international with 15 caps to his name - joined reigning European and Bundesliga champions Bayern Munich from Athletic Bilbao back in 2012.
His first season in Bavaria proved to be a roaring success, with Martinez helping Jupp Heynckes' side to win a historic treble that secured Bayern Munich's status as arguably the most formidable outfit in world football.
While Martinez evidently remains an important player for the German outfit, he has often found regular first-team starts a little difficult to come by since compatriot Pep Guardiola took the helm.
With just 17 appearances in La Liga this season, it rather appears that Guardiola - whose side were denied a place in another Champions League final following their surprisingly one-sided defeat to Real Madrid last week - does not view World Cup and European Championship winner Martinez as quite as important as the likes of Bastian Schweinsteiger and Toni Kroos.
Whether Arsenal boss Arsene Wenger will be willing to pay the fee necessary to entice Bayern Munich into selling Martinez remains to be seen, however.
While £28 million may seem like a perfectly reasonable price for such a talented player in the expensive world of the modern game, Wenger and Arsenal have taken a rather frugal approach to spending in recent years and will clearly not be forced into paying big money for average signings.
However, last summer's club-record purchase of German playmaker Mesut Ozil - who moved to the Emirates Stadium from Real Madrid - proved that Arsenal could be willing to loosen their grip on the pursestrings if a player becomes available who could have a significant impact upon the team's fortunes.
Martinez - renowned for his workrate and passing ability - could fit the bill perfectly in North London.
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