I think the answer is in the negative, and this is my reasoning:
It is trivial to see that selfish actions could be regarded as selfless under certain circumstances and perspectives. However, a not so trivial case would be one where one acts in a selfless manner, but such actions could be considered selfish from other perspectives. E.g Suppose I’m obsessed with being charitable (in the form of giving money away to charity) to the point where I neglect my kids on the premise that the kids I’m helping with my donations have it worse than my own kids. From my perspective (and possibly many other people’s), I’m acting in a selfless manner when I donate, but to my kids I’m being selfish insofar as I neglect them in order to satisfy my obsession for charity.
To show they aren’t mutually exclusive, it is sufficient to find a case in which both happen simultaneously.
I don’t know what part of ethics this would belong to, so I would appreciate it if someone were to correct it. Please provide the definition for selflessness and selfishness you are using when you provide your answer. Thanks in advance.