The Rangers and Islanders are among the most aggressive teams in pursuit of Jets defenseman Jacob Trouba, The Post has learned, with the Devils also in the chase.

Trouba, the 25-year-old impending restricted free agent for whom the Jets are soliciting offers, would slide into the right side of the first pair for either club. But his acquisition would come at a steep cost, both in terms of personnel going the other way in a trade package and the long-term contract Trouba would command.

Winnipeg, according to several sources, has yet to give permission to inquiring clubs to speak with Trouba’s agent, Kurt Overhardt, about a contract. One would figure seven years at up to $7.5 million per season for the Michigan native — who recorded 50 points (8-42) last season, 13th most among defensemen. His 42 assists tied for ninth among blue-liners.

There are up to a dozen teams in the chase for Trouba, a mobile, 6-foot-3, 220-pound puck mover, transporter and power-play guy. The Jets, who are facing a serious cap crunch, are believed to be looking for a first-rounder and a pair of legitimate prospects or young NHLers in return.

The Rangers, of course, own Winnipeg’s first-rounder at 20th overall, as part of the bounty — Brendan Lemieux, too — obtained in the lend-lease deal for Kevin Hayes. General manager Jeff Gorton, whom we are told is pushing mighty hard for Trouba, could offer that pick, impending restricted free agent Pavel Buchnevich and, perhaps, Nils Lundkvist to the Jets.

That might not be enough, not with Lou Lamoriello lurking … and, for that matter, Ray Shero, as well. Both the Islanders and Devils are loaded with prospects who might be expendable in a deal for Trouba, who has played six seasons in the NHL out of the University of Michigan following his 2012 ninth-overall selection by the Jets.

Question: Does the price become too high for the Rangers if the Jets demand Lias Andersson be included in the package?

For the Islanders, would Lamoriello be willing to include defenseman Noah Dobson, last year’s 12th-overall pick, in a deal for Trouba. For the Devils, would Shero be willing to send Jesper Bratt and Jesper Boqvist or Ty Smith back the other way? Smith, almost certainly not.

The Rangers line up with Kevin Shattenkirk, Adam Fox, Tony DeAngelo and Neal Pionk on the right side. It is difficult to imagine Shattenkirk — at a $6.65 million cap hit — remaining if the Blueshirts add Trouba, who would presumably split the power-play quarterback responsibilities with Fox, the rookie out of Harvard whom the Rangers acquired from Carolina in April.

The first buyout period opened on Saturday, with the Rangers quiet. They could trim payroll by moving Jimmy Vesey ($2.275 million) and/or Vlad Namestnikov ($4 million), though the team will need people to play up front.

Or, they could go the buyout route with Shattenkirk and/or Brendan Smith ($4.35 million). Buyouts of both would represent a cap saving of approximately $7.47 million, though generating a combined $2.6 million of dead cap space down the line. There is time for those decisions — if not by the June 30 deadline, then during the second summer buyout window following arbitration filings.

But as the entry draft looms next weekend in Vancouver with the July 1 opening of the free-agent market — looking at you, Artemi Panarin — not all that far behind, the Rangers are working hard to land Trouba.

They’re not the only ones.