It doesn't appear so. From the Wikipedia page for the first movie in the rebooted series:
In August 2009, 20th Century Fox announced a reboot of the Fantastic Four film franchise.
According to 20th Century Fox's consultant for their Marvel Comics based films, Mark Millar, it would take place in the same universe as the X-Men film series.
Furthermore, the Wikipedia page for movies within the Marvel Cinematic Universe doesn't mention the Fantastic Four reboot.
An article from "The Daily Beast" speculates that Marvel may be trying to undermine the success of the rebooted series:
Since 20th Century Fox owns the film rights to both the Fantastic Four and X-Men franchises (the latter acquired back in 1993), thus excluding them from the tethered MCU ecosystem and granting them limited financial windfall, the Disney-owned superhero behemoth Marvel has undertaken a series of covert actions against these two valuable properties.
Last October, Marvel Comics announced at New York Comic-Con that it had abruptly canceled the Fantastic Four comic book series. “We had heard that Marvel wanted to use the Fantastic Four characters in future Avengers films, so it could be a way for Marvel to put pressure on the studio,” wrote Deadline at the time. The Avengers’ two-part film finale, dubbed Infinity War, hits theaters in 2018 and 2019, and in the comics, the Fantastic Four play a substantial role in the apocalyptic proceedings—as does Spider-Man, though Marvel managed to strike a deal in February to share custody of the web-slinger with Spidey’s licensee, Sony.
If that weren’t enough, last November, Marvel decided to kill off most of the members of Trank’s Fantastic Four movie ensemble—Teller, Mara, and Bell—in a Fantastic Four comic. Yes, they literally blew up the actors in the comic, right after they referred to their director as “Trang” and speculated on the film’s planned sequel, set to hit theaters in 2017. Oh, and Marvel has taken it upon themselves to retroactively erase the Fantastic Four (and X-Men) from comic book covers and T-shirts of its famed ’80s series Secret Wars.
It would appear that Marvel is less than pleased with Fox owning the Fantastic Four movie rights.
The Fantastic Four, at least on movie screens, are the property of Fox Studios. There is, however, an interesting deal between Marvel and Sony Studios regarding Spider-Man: Sony had been the owner of those movie rights, but when Marvel decided to use Spider-Man in an upcoming film, they came to an agreement with Sony. Basically, Sony will work with Marvel on the soon to be released Sony Spider-Man film, structuring the character and storyline in such a way that Marvel will be perfectly positioned to use the character in their own, much further off movie (which will be a kind of Superhero battle royal).
It is extremely unlikely that Fox and Marvel/Disney will come to the same sort of agreement over the property rights to Fantastic Four, because Marvel/Disney and Fox don't get along very well. In fact, Marvel/Disney has been doing everything in its power to mess up the release of the FF movie, up to and including killing off characters, putting the comic book series on hold ahead of the movie release date, and removing the likeness of the Fantastic Four from their products.