The German champions have held a long-standing interest in Sane and were heavily linked with a move for the attacker last summer, only for Sane to stay at the Etihad Stadium and subsequently suffer a knee ligament injury which has sidelined him for the entire season so far.
More recently Bayern have also been linked with Werner, who is thought to be Liverpool's top transfer target, and Matthaus believes that the striker would be a better fit for Hansi Flick's side than his international teammate.
"My soft spot for Timo Werner is well known. And I don't mean to say that I don't think Leroy Sane is great. But you get the feeling that Flick and [Oliver] Kahn are more likely to see Timo Werner as the player who could be better suited to this club," Matthaus told Sky Deutschland.
"He is more flexible in the field, his character may correspond a little bit more to the wishes of those responsible. The risk of agitation is significantly lower. He can play at the very front in [Robert] Lewandowski's place, hanging behind or on the wings. And he should also be cheaper.
"I don't understand why they didn't sign him before when he was on a silver platter. But better late than never. He has clearly developed again this season. Sane was unable to make up ground due to his long injury. Both players would be total added value for Bayern. But if I had to choose today, I would be making room for Timo Werner."
Werner has directly contributed to 28 goals in 25 Bundesliga appearances this season, a tally only Jadon Sancho can beat. body check tags ::