There have been many discussions about whether or not Quicksilver should be in the next X-Men film or the next Avengers film. Quicksilver is a mutant, but he has been mostly featured as a member of The Avengers. Coming from someone who learned about superheroes from the original cartoons, I only remember Quicksilver from the X-Men: Evolution series. That should establish him as a X-Men character to me, but there could be a way to use Quicksilver as a way to bridge the gap between the X-Men universe and the Avengers universe.
We would all love to see Wolverine or any of the other X-Men in the MCU, but with so many X-Men films that have already established one universe with a questionable timeline, it would be very difficult to connect the two. X-Men: Days of Future's Past seems to deal with time travel and an event that makes mutants a target in the future. This is based on a famous story line from the comics, but Fox will of course make changes to it. If these changes could be used to bring the X-Men universe into the Avengers Universe, I think some fans would be willing to forgive them.
The biggest difference between the two universes is that in X-Men mutants are a publicly known situation, but that does not seem to be the case in the Avengers. In the X-Men films, it is a big part of the world that there is debate over where mutants belong in society. This cannot be something that is just ignored in The Avengers. Assuming that most of the X-men films and Avenger films take place in the year they were released, it would seem weird that none of the events in either film affected each other. Maybe the events of X-Men: DOFP could change the events of later X-Men films.
In X-Men: First Class, which took place in the 60's, the mutant situation was not a public issue. X-Men: DOFP takes place in the 70's, and the mutant situation will most likely still not be known to the public. After an event, like the president being assassinated, mutants become public knowledge and starts the mutant debates. If this event is averted, the mutant situation could be kept away from public eye for longer. What if because the X-Men worked with the government in the 70's to prevent an incident, the government decided to start a new program to keep people with superpowers out of public eye. This could mark the beginning of S.H.I.E.L.D. It would also delay the reveal of mutants to the public until possibly the beginning of The Avengers 2. At the beginning of The Avengers 2, there could be news reports showing that because The Avengers are publicly known, many mutants feel that they should be known too. This could lead to mutants using their powers in public and wanting to not have to hide anymore. The public would be more worried about the mutants though because they would be uncontrollable. The Avengers at least work with the government, so that would provide some comfort to the public.
This would lead to the introduction of Quicksilver and Scarlet Witch. They are both mutants, and they would want to join the Avengers to prove that not all mutants want to abuse their powers. Some mutants do want to help humanity. If it is also established that they are the children of Magneto, that only adds more to what they are trying to prove. They are the children of the leader of the Brotherhood, but they still want to help humanity.
This also leads to one other problem. Quicksilver and Scarlet Witch will most likely be in their early 20's in The Avengers 2. This would mean that they were born in the early 90's and Magneto was in his 50's when he had his children. There is one radical thing that could be done to fix this. Since X-Men: DOFP features time travel, Magneto and Professor X do not have to go back to the 70's. They could use time travel and start new lives in the late 80's or early 90's and they would still be in their 30's. Professor X's school would still be established in the 60's, and it would seem like he disappeared for 20 years and reappeared without aging. He could still teach his young students, like Cyclopes, in the early 90's so they would be in their 30's in the 2010's. Magneto would go his separate ways knowing that mutants would be kept a secret for a while longer. This would lead to him having kids in the early 90's.
This seems like a radical thing to do, but it does fix the timeline. This also allows the younger actors of X-Men: First Class to be in the MCU. I am sure that Marvel Studios would love to have Jennifer Lawrence or Michael Fassbender in there movies. These are big name actors Marvel Studios can use to sell their movies, so they do not have to always rely on Robert Downey Jr.
All this is very unlikely to happen, but at least there is a way for it to happen. X-Men: DOFP has so much potential to change everything. This would only leave Spider-Man and the Fantastic Four out of the MCU. If Fox is willing to bring an establish universe into the MCU, they should have no problem bringing in a rebooted Fantastic Four universe into the MCU. There is also rumors and speculating that The Amazing Spider-Man is already in the MCU. With all the Marvel properties in the MCU, there is unlimited potential for Marvel comic book movies moving forward.