Her name has long been mentioned in discussions of who could best portray the fan favorite character, and in an interview with MTV back in 2015, the topic actually came up. It seems that Larson isn't that familiar with the character, however, and possibly got the character confused with DC's Captain Marvel, better known as Shazam, as her first thought was: "To play, isn't that a boy?"
The interviewer gave Larson a few more details, but she still wasn't familiar, saying:"The first female, so would I be playing a man? (laughs), I was like this is interesting, I'm kind of into it. I thought I was always forever going to be stuck playing female roles but, I'm down to play Chris Evans. No, wait, Chris Evans is Captain America. Who's Captain Marvel?"
After a brief pause, the actress still couldn't place the character, but would still be up for the role if that is what fans want to see, adding: "no idea what I'm talking about, great, but people want me to this? Okay, good to know. I guess I've got to start reading the comic book."
Whether she has previous knowledge of the character or not, I still think she'd be great in the role. You can see what she might look like as Captain Carol Danvers thanks to artist extraordinaire Boss Logic here.