Both teams you mention need other potential players. But Bayern Munich does not need a striker now, or let me say, it is not necessary for Bayern Munich to get any players in my opinion. because they have all the positions and they are still strong, so they don't need anything like that now.
If you think Bayern Munich don't need a striker right now, then why are they so adamant in bidding for Harry Kane this summer? isn't it obvious they are not so confident with the current squad even though everything feels very complete. Moreover, competing with other strong teams in the champions league is not an easy matter if a team doesn't have a mature striker and I think whatever the reason, Bayern Munich will still be looking for a new striker if later they don't manage to get Harry Kane.
So far Bayern Munich has 2 center forwards, namely Eric Maxim Choupo-Moting and Mathys Tel. The two attackers were played alternately by the coach and both had good goal contributions last season. I think Bayern Munich want to sign a new centre-forward because they realize that Choupo-Moting is no longer young. He is already 34 years old although he has good form.
Apart from the two centre-forwards I mentioned, the Bayern Munich coach often gives my player or the second striker the opportunity to occupy the center forward position. Sometimes that's good, but it would be great if Bayern Munich had a pure centre-forward instead of doing some experiments on wingers and others to become a centre-forward. Kane is a good fit, but so far nothing is certain.
Bayern Munich are desperately in need of a top 9, that is one wing they're yet to strengthen since the departure of Lewandowski and I think that's why they'll do anything to get Harry Kane this summer and to challenge for the champions league trophy they're are several area they still need to strengthen, though it a pre-season friendly game but if you observed the match against Manchester City you'll understand that they're lacking a good goal getter because Choupo-Moting is not very young and capable giving a good number of goals though they still got sane in their squad but won't really on him only to deliver the goals.
That's why they're fighting tooth and nail for Harry Kane signature cause they need such a player of his quality and would deliver up to 20 goals plus next season and would help them challenge for the champions league cause that's one trophy they'll be looking to get next season, experimenting with their wing option might favour them but they won't rely on that when they'll be facing other big teams like Manchester City or Realmadrid.