FOXBOROUGH, Mass. – In 2006, New England Patriots kicker Adam Vinatieri was an unrestricted free agent and it was hard to envision him winding up in an Indianapolis Colts uniform. He did.

In 2013, Patriots receiver Wes Welker was exploring offers from other teams and got into deep discussions to sign with the Denver Broncos, yet it was hard to envision him following through on it. He did.

Those two examples came to mind when the question was asked: Would New England linebacker Dont’a Hightower really sign with the New York Jets?

It’s a timely question because Hightower is visiting the Jets and the meeting is expected to wrap up Monday, according to Jason La Canfora of CBS. It is believed to be Hightower’s first visit of free agency, as a market for him didn’t develop as quickly as many projected.

If Vinatieri and Welker could cross enemy lines, there’s nothing that says Hightower couldn’t.

That’s why, even though some around the NFL believe Hightower ultimately will re-sign with New England, there are no guarantees when it comes to free agency. As ESPN analyst Tedy Bruschi said last week, this is “truth week” in the sense that you learn a lot about how teams view players, and vice versa.

Hightower has been part of two of the best programs in football over the last nine years – first at the University of Alabama under Nick Saban and then with the Patriots under Bill Belichick. Both are similar, hard-driving cultures, and now this is Hightower’s chance to explore what it might be like in a different environment.

It wouldn’t be a surprise if that was part of the sales pitch from one of the Jets coaches who would work most closely with Hightower, Mike Caldwell. The Jets’ inside linebackers coach/assistant head coach is a former linebacker who broke into the NFL in 1993 on Belichick’s Cleveland Browns team, with Saban as his defensive coordinator, so he’s walked in the same football shoes Hightower has. Maybe that leads to a connection that Hightower is interested in investing in, as the Jets have been exploring an upgrade at his position.

Ultimately, it figures to come down mostly to financial investment.

Whatever the Patriots have on the negotiating table for Hightower hasn’t been enough for him to want to sign the deal at this point. That led him to the visit with the Jets, and maybe they wow him with an offer that’s too good to pass up.

If they don’t, sometimes simply getting a peek behind the curtain with another team can spark more appreciation for a player’s original team -- or get them to up their original offer and be a catalyst to re-sign. Other times, it can work in the opposite direction.

Which one will it be with Hightower?