I've experienced the same issue.
Started a save at Bayern, in the first transfer window T.Müller got unhappy because of lacking depth at center back.
bought a 3-4 star central defender, which did not resolve his issue
issue resolved itself after the transfer window (it said hes happy with the depth now, even though the window was long closed)
winter transfer window and T,Müller is unhappy again, same reason as before.
Might be of note: one of my centre backs is currently on international duty (Asian Nations Cup). maybe that is affecting it?
I've uploaded a save before Müller got unhappy - "Bayern - Müller happy.fm" and one after the issue - "Bayern - Müller unhappy.fm"
As general feedback, in the conversation a simple "we don't have budget for that" option is missing for me. I'm not gonna be able to get squad depth with 700k transfer budget.