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Let's say that you say 'nerd' meaning someone who's pretty smart. Now that doesn't mean you have a face full of pimples or greasy hair. What it means is that your academically performing. AND THAT'S WHERE IT ENDS. It does not dictate your looks or you hobbies. It is possible to be smart and like sports. Being a 'nerd' myself, I don't fit the stereotypical profile either. I listen to metal, punk and edm. I do art. I'm a language student. I currently have my hair dip dyed blue. I don't wear glasses and no longer have braces, and all of my best grades came after I got my braces off anyway. So in a nutshell, yes, it is possible.
My definition of nerd is not the common stereotype. To me, a nerd is someone who has a very deep and passionate interest in something and dedicates lots of their time to that one thing. Really, you could be a nerd of multiple things! You could be a nerd of computers, of games, of sports, of literature, of filmography - or more specifics, such as a nerd for a certain sport or a certain series of movies or books. So yes, in conclusion, I think someone can be "both a nerd and sports fan", even if you're judging by the stereotype.
Anyone can do anything. If you would define a nerd as a "smart" person, then I would say that I know a lot of really smart and really athletic people. I have a friend who is on a girl's hockey team and is trying out for junior olympics, and she always gets straight A's in school and is one of the smartest people I know. It's a free world, after all, and nerds being unathletic is really just an untrue stereotype.