The 31-year-old actor has been cast in the untitled film that has been penned by Haynes together with Phoenix and Jon Raymond.
Details regarding the plot are scarce, but the picture is said to follow two men - one of whom is played by Phoenix - who are intense lovers and leave California for Mexico.
Haynes' regular collaborator Christine Vachon is producing alongside Pam Koffler.
Danny played the role of Lieutenant Mickey 'Fanboy' Garcia in 'Top Gun: Maverick' and expressed hope that he would be able to reprise the part in a third film in the action franchise.
He told Variety: "Obviously, it'd be amazing to be able to do a third film in this beautiful story. But, as we learned with the second one, it's got to be absolutely right.
"Being cognizant of that, we're excited at the prospect of everyone back in the air. I'm having withdrawals. And also playing Falcon (in the Marvel Cinematic Universe) at the same time. Me and the skies..."
The 'Oh My Block' star explained that working with stars such as Tom Cruise has helped him develop in all aspects of the film industry.
Danny said: "One of the biggest blessings of being in elite circles with the most brilliant minds in storytelling, is that you're then endowed with all this knowledge that this small little group has, and they pass it down.
"So someone like Tom (Cruise), he is so accessible. If I have a pitch deck, I send it to him, he's the first one to send me notes. Having that access then becomes a responsibility.
"My next step as a filmmaker is to be able to take that same knowledge that I'm learning and being able to pass it down, because experience is sometimes everything."