The ex-British Lions wing has been based in Florida since January as part of the NFL's International Player Pathway (IPP) program.
Along with 10 other international prospects, Rees-Zammit has been undergoing a 10-week crash course in the rules and skills needed to switch to the NFL.
An NFL source said that after accepting invites from the two interested clubs, Rees-Zammit was also expected to have visits with other teams.
The Welshman is the biggest name to have left rugby to attempt to make it in the NFL.
One first step that may be open to Rees-Zammit is to earn a place on an NFL team's summer training roster which could lead eventually to a full roster spot or a place on the practice squad.
Before his trial Rees-Zammit said he was hoping to show he could play in a number of possible roles on a team.
"I want a coach to look at me and be like, well, he can play multiple positions, he's not just a receiver, not just a running back and can play a lot of positions," he told AFP in an interview.
"You can play a lot of roles within the offense because there are many players like that now," he said.
The most successful convert from rugby to American football is Australian offensive tackle Jordan Mailata who reached the Super Bowl with the Philadelphia Eagles in 2022 and was named as a Pro Bowl alternate for the past two seasons.
Mailata recently spent four days working with Rees-Zammit and other hopefuls at the IPP training camp at the IMG Academy in Bradenton, Florida.
