The Pro Bowl wide receiver was recently released by the Arizona Cardinals, clearing the way for Hopkins to join another team for the upcoming season.
During a Browns charity golf tournament, Watson hinted that he's informed Cleveland's front office that he would like for the team to make a run at Hopkins.
"That's kind of out of my range of things," Watson said. "All I can do is make a call and see what happens."
Hopkins had been representing himself but has hired Klutch Sports to represent him.
Hopkins, 30, was a three-time All-Pro receiver playing with Watson in Houston. In 2020, their last season together, Hopkins finished with 104 catches for 1,165 yards and seven touchdowns.
His last two seasons with Arizona, Hopkins combined for just 106 catches over 19 games. Several teams are expected to pursue Hopkins, including other AFC rivals.
"Me and D-Hop, we just naturally talk," Watson said. "We've been talking since the Houston days. ... He's always been a brother of mine. ... Our connection, our relationship has always been great. ... Of course, we would love to have him. He knows that."
In an interview last week with the "I Am Athlete" podcast with Brandon Marshall, Hopkins said he's looking for three things in a team at this stage of his career -- stable management, a quarterback who "loves the game like I do" and "a great defense."
"I'll just say this, D-Hop, DeAndre Hopkins would love to be in a place where the opportunity is there for us to win," Watson said Tuesday. "We check all those boxes and I think for us to know and make sure we check all those boxes on the national stage, we've got to go out there and prove it and I think D-Hop would love to be a part of that."
Coach Kevin Stefanski would not comment on the team's interest in Hopkins, saying he was pleased with some of its offseason additions.
"I really, really like our wide receiver room," Stefanski said. "I love the guys that are in there. [General manager] Andrew [Berry] and his crew are always looking at every avenue and that type of thing, so I won't comment specifically on the player other than to say I really like our roster."
The Associated Press contributed to this report.