As Wikipedia says -
Prometheus was originally intended as a direct prequel to the 1979 science
fiction horror film Alien, set approximately 30 years before the
events depicted in the film. While the finished film explored a more
stand-alone mythology based upon the race of giant beings discovered
by the crew of the Nostromo in Alien, it is, as acknowledged in the
end credits, based on elements from the original film.
As stated in Alien vs. Predator Wikipedia page
In a 2002 interview, Scott's concept for a story was "to go back to
where the alien creatures were first found and explain how they were
created"; this project eventually became Scott's 2012 film Prometheus.
On learning that Fox intended to pursue Alien vs. Predator, Cameron
believed the film would "kill the validity of the franchise" and
ceased work on his story, "To me, that was Frankenstein Meets
Werewolf. It was Universal just taking their assets and starting to
play them off against each other...Milking it." After viewing
Alien vs. Predator, however, Cameron remarked that "it was actually pretty good. I
think of the five Alien films, I'd rate it third. I actually liked it.
I actually liked it a lot." Conversely, Ridley Scott had no
interest in the Alien vs. Predator films. When asked in May 2012 if he
had watched them, Scott laughed, "No. I couldn't do that. I couldn't
quite take that step.
It's clear that Ridley Scott never in a favor of
Alien vs. Predator Franchise and that's the reason that his film
Prometheus only connected to Alien Franchise, it doesn't have any connection to
Alien vs. Predator films.
As stated in Prometheus Wikipedia link
Development of the film began in the early 2000s as a fifth
installment in the Alien franchise. Scott and director James Cameron
developed ideas for a film that would serve as a prequel to Scott's
1979 science fiction horror film Alien. By 2003, the development of
Alien vs. Predator took precedence, and the project remained dormant
until 2009 when Scott again showed interest. Spaihts wrote a script
for a prequel to the events of the Alien films, but Scott opted for a
different direction to avoid repeating cues from those films. In late
2010, Lindelof joined the project to rewrite Spaihts's script, and he
and Scott developed a story that precedes the story of Alien but is
not directly connected to that franchise. According to Scott, although
the film shares "strands of Alien's DNA, so to speak", and takes place
in the same universe, Prometheus explores its own mythology and ideas.
So it's clear that Prometheus is a sequel to first alien film and their may be one more Prometheus film which will fill the gap between First Alien film and Prometheus and AVP's is just like a spinoff.