Warning – Minor SPOILERS lie ahead for Deadpool. If you have not seen the movie and want to, I recommend not reading this article yet.
Alright, with that out of the way, I need to say one more thing: I don't personally believe this theory, but I think it's a very fun topic and it would be very interesting if it was true. But, I think it is possible that this movie could exist along with the likings of Iron Man and Captain America: The Winter Soldier, and that Deadpool exists along with Thor, Ant-Man, and Nick Fury (Wade even made a reference to Sam Jackson in an eyepatch).
Okay, I don't have too much evidence for this, but I think it's enough to make a fun article! And I am ignoring all "They don't own the rights to that character" stuff (not commenters, I'll likely get back to them), because let's face it: it really isn't true. My first piece of evidence is...
What if the X-Men movies are just movies in the MCU?
My main point with this is the Professor X reference in Deadpool. Colossus tells Wade Wilson that he needs to see the Professor, and Wade says "Stewart or McAvoy?" This, of course, is a reference to the two actors that have played Professor X in the X-Men film series. It's possible that Wade Wilson was just a normal person who existed in the MCU, and he saw the X-Men movies, and he knew about James McAvoy and Patrick Stewart's performances of Xavier.
Bob, Agent of HYDRA
The makers of Deadpool snuck in a cameo of one of Deadpool's best friends, Bob, even though they didn't legally own the rights to him. Personally, this was one of my favorite moments of the movie, as I instantly recognized Bob when Wade said "Bob?!" But what if Bob actually is an agent of HYDRA? Or he was or will be? I think that would be a very different way to think of it. It's possible that Bob was there in 2014 when HYDRA took over S.H.I.E.L.D. and he might have just became a henchman of Ajax (not the dish soap). It's also possible that HYDRA ordered him to work with Ajax for some reason; maybe to find the new Mutant superhero, Deadpool!
It would explain Quicksilver and Scarlet Witch
Quicksilver and Scarlet Witch's origins haven't been fully explained, but I don't expect them to be. They might have been part inhuman, mutant, and they were experimented on with Loki's staff, but it's confusing to me. All that I know is that they were different, mutants, but they can't call them that. If Deadpool existed in the MCU, it would explain that these two are mutants, even though they can't say that.
The (possible) Helicarrier
Did anyone else notice that the giant aircraft at the end of the movie looked like a Helicarrier? I did, and it just helps this article. Yes, I know, it was probably just another type of aircraft, but it did look suspiciously like a Helicarrier. So, what if this was a Helicarrier that S.H.I.E.L.D./HYDRA owned but when HYDRA revealed themselves, the Helicarrier above New York City (where Deadpool takes place) came crashing down? It would be a very cool twist, at least I think so.
So could mutants, Deadpool, Colossus, and Negasonic Teenage - what the sh*t - Warhead exist alongside the Avengers?
I think it's possible that the new movie could be a part of the Marvel Cinematic Universe. I don't think there's too much evidence pointing to either option, but like I said, it's still a very fun and interesting idea! Plus, that would mean that the great characters introduced in Deadpool could eventually be Avengers or their villains!