I want to have a related list 'Partnership Managers' on the Account object. All the partnership managers comes from the User object. For example, one account can have multiple partnership managers (users). When I try to create a lookup field on the User object, I don't see any such option. Is there any way to achieve this goal?
User object can only have Hierarchical relationships. There are a couple of ideas you can vote here and here. You can create a junction object between a user and account if that suits the requirement as mentioned in the comment above. That way a user can be related to multiple accounts.
Have you thought about using Account teams?
Do note that there will be impact on reporting and your apex code will need to be architected accordingly.