Charles Robinson of Yahoo Sports spoke to a source familiar with the filing who said Trump is "the crystal-clear target in the complaint."
The suit will point to Trump's rhetoric regarding national anthem protests, saying the sitting president's pressure on the topic led to owners refusing to sign players who knelt or sat during the anthem.
Reid was the first player to join former teammate Colin Kaepernick in his national anthem protest in 2016. Kaepernick filed a lawsuit last year claiming owners colluded to keep him out of the league.
Reid said in December he understood it was a "possibility" his anthem protests would limit his free-agency options.
"I would say I understand that's a possibility," Reid told reporters. "And I'm completely fine with it. The things that I've done, I stand by, and I've done that for my own personal beliefs. Like I said, I'm fine with whatever outcome happens because of that."
Much like Kaepernick, Reid has a history of NFL success. He was a starter for 69 of his 70 NFL games, including 12 contests last season. He recorded 52 tackles and two interceptions.
The complaint alleges Trump had both indirect and direct contact with NFL owners in order to influence them against signing any player who protested during the anthem. Trump has been a vehement critic of those who he feels disrespect the anthem, famously calling on the NFL to fire or suspend any player who protested.
His rhetoric led to a massive protest from hundreds of NFL players in September.