One of the players with the potential to be the Jets’ starting quarterback in 2017 visited the Giants on Saturday to talk about becoming their backup.

Geno Smith, a former Jets second-round pick and a free agent, visited with the Giants, a source confirmed. The Record of New Jersey first reported the visit.

It’s unlikely that the Giants will be in a rush to sign Smith, who still is recovering from ACL surgery after injuring his knee last season. The visit, which began in the afternoon and continued through dinner, included mostly meetings and medical checkups and did not involve any physical workouts, the source said. It was more likely to gauge his recovery and his willingness to back up Eli Manning.

Last month, on NFL Network, Smith said he would be willing to take that back seat. “I’m open to it,” he said. “That’s not my goal . . . I was brought into this league, I was brought to the Jets, to be a certain caliber of player, and being injured for two years has kind of taken that away from me. My mistakes were shown on the field my first two years, then me getting better has kind of been behind the scenes.”

Smith has had a rocky career with the Jets. He started all 16 games as a rookie in 2013 and 13 games in 2014. Before the start of the 2015 season, he was punched in the face by teammate IK Enemkpali and suffered a broken jaw. He appeared in only one game that season, replacing Ryan Fitzpatrick.

Smith began last season as Fitzpatrick’s backup. He was named the starter for Week 7 but tore his ACL in that game. He has said he expects to be ready to participate in training camp.

In 33 games with the Jets, Smith has thrown 28 touchdown passes and 36 interceptions. Neither he nor the team has closed the door on his re-signing to compete with Bryce Petty and Christian Hackenberg.

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While the Jets are without a clear starting quarterback, the Giants are looking to add a backup to Manning. They currently do not have a proven one on their roster (Keith Wenning, who has never played in a regular-season game, is on the team). General manager Jerry Reese has said the team will try to identify an eventual replacement for the 36-year-old Manning this offseason. At the very least, they will need healthy arms (and knees) for OTAs and minicamps that begin in May. Smith might not be able to provide that if he still is rehabbing his ACL at that time.

If the Giants do add Smith, it would be the third such defection from the Jets in a little more than a year. The Giants signed defensive tackle Damon Harrison last offseason and signed recently released receiver Brandon Marshall last week.

Fluker in, too. Smith wasn’t the only free-agent guest of the Giants on Saturday. They also hosted offensive lineman D.J. Fluker, recently released by the Chargers. The former first-round pick could give the Giants depth and compete at either guard or tackle. Because of the Giants’ constraints under the salary cap, they were unable to compete at the high end of the offensive line market . . . Marshall Newhouse, who started 20 games for the Giants in the past two seasons, mostly at right tackle, signed a two-year deal with the Raiders on Friday night.

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