Head-canon you’ve accepted that, while not necessarily supported by canon, isn’t contradicted by canon either
My answer to this question can be summed up in one word — Wolfstar. For those who don’t know, Wolfstar refers to a romantic relationship between Remus (Wolf) and Sirius (Star) in the Harry Potter universe.
Many shippers have convinced themselves that this relationship is canon. Their arguments are nicely collated on the LiveJournal account, never met anyone like you, and HPfanfiction on Reddit. I, however, disagree.
While I am not inside Ms. Rowling’s mind and cannot, therefore, state what she was thinking when writing Harry Potter, I do not believe she ever intended to make Wolfstar canon. At best, they have a brotherly relationship. At worst, it may be another instance of Queerbaiting, something Rowling has been accused of more than once.
However, while a romantic relationship between Remus and Sirius is not necessarily supported by canon, there is nothing in the books which directly contradicts such a relationship.
Thus, today’s question has a simple, one word answer. Wolfstar.