Tim Tebow may still have a future in the NFL after all.

The New England Patriots seem to think so and plan to sign him on Tuesday if he passes a physical.

He won’t be a starting quarterback, of course, with Tom Brady on hand in Foxborough. But certainly he’s an intriguing reclamation project — yet another chance for coach Bill Belichick to torture the New York Jets, who failed to find a role for Tebow last season.

And that could make for quite a Boston Tea-bow Party.

A person familiar with the situation told The Associated Press on Monday that Tebow will join the Patriots’ minicamp on Tuesday and sign with the team, pending the medical exam. The person spoke on condition of anonymity because no official announcement had been made. Even when Tebow signs, there is no guarantee he will play for the Patriots.

ESPN first reported that Tebow would sign with New England.

Former Broncos general manager Ted Sundquist sees the logic in the move.

“If you can find a club that’s mature enough to handle it as an organization, then you’re going to find the right spot for him,” Sundquist said. “What I mean by that is all the media mania and that sort of thing. The club says, ‘Look, this is the reason we’re bringing him on. We feel he can bring X, Y, Z and A, B, C to the table.’ Explain it to Tim, explain it to the media, explain it to your fan base and explain it to your organization.”

That description seems to fit New England perfectly.

One of the NFL’s most polarizing players, Tebow spent a lost season in 2012 with the New York Jets, playing sparingly behind struggling starter Mark Sanchez. Some fans thought he got a raw deal and deserved more of a chance; others thought he lacked the skills to be a pro quarterback. He was released in April with barely a shrug — hardly the ending most Jets fans envisioned considering his super-hyped welcome to the Big Apple.

Tebow won two national titles at Florida and was a first-round draft pick in 2010 by Denver. As a rookie, Tebow threw just 82 passes in nine games, starting three. But in 2011, he started 11 games, throwing for 12 touchdowns and six interceptions, and took the Broncos to a wild-card win over Pittsburgh before an AFC divisional playoff loss to New England, 45-10.

Despite the Broncos’ playoff run, he was traded to New York the following offseason when Denver signed Peyton Manning. Tebow threw only eight passes for the Jets, completing six, ran 32 times for 102 yards and was used mostly to protect the punter.

“Unfortunately,” coach Rex Ryan said in a statement when Tebow was released, “things did not work out the way we all had hoped.”

The Patriots have Ryan Mallett as the backup to Brady; they released QB Mike Kafka on Monday.

Asked if Tebow had signed, Patriots spokesman Stacey James said, “I do not anticipate any additional transactions to announce tonight.”

Tebow’s NFL career appeared over when the Jets couldn’t trade him at draft time and wound up cutting the left-handed quarterback, who won the 2007 Heisman Trophy. But now he is headed to New England, where the man who drafted him as coach of the Broncos, Josh McDaniels, is an offensive assistant under Belichick.

And apart from winning Super Bowls, Belichick likes nothing better than sticking it to the Jets. He’s had a running feud with Ryan for nearly four seasons, in part because Ryan once said he wasn’t hired to kiss Belichick’s rings.

Belichick was Jets coach for one day in 2000, infamously resigning with a hand-written note. He soon joined New England, and has been regularly beating the Jets for more than a decade.

Revitalizing Tebow’s career would be another big step toward humiliating New England’s archrival.

Tebow has been criticized for his throwing motion but has said he wants to play quarterback, not switch positions. Still, the Patriots might need help at tight end after Rob Gronkowski underwent a fourth operation for a broken forearm and faces back surgery. At 6-foot-3 and 236 pounds, Tebow has the size to play that spot.

Belichick values versatility in his players, having used wide receivers Troy Brown, Julian Edelman and Matthew Slater at defensive back when injuries hit that position.

Belichick also has been willing to gamble on players discarded by other teams. Some have succeeded, like wide receivers Wes Welker and Randy Moss and running back Danny Woodhead. Some haven’t, including wide receiver Chad Johnson and defensive lineman Albert Haynesworth.

The media circus that surrounded Tebow in Denver and with the Jets also could be minimized by Belichick, who keeps a tight lid on players’ interactions with reporters.

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AP Sports Writers Dennis Waszak Jr., and Howard Ulman contributed to this story.