The Chile international is soon to enter the final 12 months of his Emirates Stadium contract and has no current plans to open talks with the Gunners.
Arsenal could be prepared to cash in on their star man, who again proved to be the matchwinner in Sunday's FA Cup semi-final showdown against Manchester City with his 24th goal of the season, rather than allowing him to leave for free the following year.
Matthaus has urged Bayern to consider making a big-money offer for the 28-year-old, citing his versatility as a key reason why he will potentially be such a success in Bavaria.
"Sanchez is a great player, he would be a good signing for Bayern," he told AZ. "His biggest pro is that he can play in a central role up front and on the wings.
Matthaus spent 12 years with Bayern across two separate spells in his playing days, while also representing Borussia Monchengladbach and Inter Milan.