Watson, ranked No. 7 in the world, is not a member of the team. Davis Love III has one remaining captain's pick, to be announced after next week's Tour Championship.
Six to eight members of the U.S. squad are expected to tee it up with three or four players who are not on the team, Love told Rosaforte. One of those players is Watson. Daniel Berger, Justin Thomas and Jim Furyk are the others expected to join the outing who are not currently on the team.
Rosaforte said he asked Love if Watson has not been picked because of any issues with his personality. In a 2015 ESPN poll of 103 anonymous Tour pros, Watson was chosen as the player others would be least likely to help in a fight.
Love said Watson is "the opposite of that," Rosaforte reported, and is a popular presence in the team room. "He's quirky, but so is Phil [Mickelson,]" Rosaforte said Love told him.
"I told Bubba after the Olympics, remember, there's a pick after the Tour Championship," Love said he told Watson.
The last captain's pick is informally known as the "Billy Horschel pick," after Horschel in 2014 got hot at the end of the season, winning two playoff events and the FedEx Cup, but was locked out of the Ryder Cup team because the captain's selections had already been made.
"If he plays well, he's certainly going to be considered," Rosaforte said. "He is not as negative an influence as many people wrote and led us to believe over the last couple of days, at least coming from captain Davis Love."
The 41st Ryder Cup matches will be played Sept. 30-Oct. 2 at Hazeltine National in Chaska, Minn. Europe has won the past three Ryder Cups and six of the past seven.