The Islanders’ relationship with Barclays Center has been on such thin ice during the club’s first season in Brooklyn that both sides are secretly exploring ways to cut ties or modify the existing terms of their lease, The Post has learned.

The Islanders were losing roughly $20 million annually playing at the antiquated Nassau Coliseum — their home for 43 years — when owner Charles Wang in 2012 cut a 25-year lease deal with Barclays Center to have the team move there beginning this season. The lease includes a little-known out clause that kicks in after the fourth season that both sides could take advantage of, sources said.

“I don’t think either side ever believed the full lease would be honored,” said a source briefed on the matter. “I just didn’t think we’d be talking about this the first year in.”

Although the Islanders own one of the NHL’s top home records, their fans have been quite sour about the move, complaining about obstructed-view seating, jacked-up ticket prices, the nixing of longtime team traditions and feeling like second-class citizens in a building monopolized by the NBA’s Nets.

Jonathan Ledecky — who heads a group of investors set to replace Wang as the team’s majority owner July 1 — apparently is listening. A source close to the Islanders and other industry sources say he’s enamored with possibly moving the team to Queens or back to Long Island.

In either scenario, a new arena likely would have to be built — an expensive proposition considering it cost $1 billion to open Barclays Center in 2012. Another option is renegotiating the Barclays Center lease to salvage the relationship, sources said.

Nets and Barclays Center owner Mikhail Prokhorov is overseeing a $260 million renovation of the Nassau Coliseum to make it state of the art by next year. However, the plans include trimming seating at the Islanders’ former home to 13,000 — which would make it too small to host NHL hockey full time.

Willets Point in Queens previously was floated as a possible landing spot for the Islanders. The idea gained little traction before the team opted to move to Brooklyn.

Under the lease deal, the Islanders agreed to relinquish control of the business side of operations to get out of the red — a rare setup for any pro sports franchise. Barclays Center agreed to pay the Islanders an average lump sum of $53.5 million annually with the arena making its money off ticket and suite sales, sponsorships and other promotions, sources said.

“The Islander deal was forced from the start because the club was hemorrhaging so much money playing on Long Island … and had to bail,” another source said. “Now you’re left with this weird situation where Barclays’ folks pay the Islanders to play there — but aren’t getting the bang for the buck they desired, not to mention all the crap they’re getting from Islander fans who are finding every little fault they can with being in Brooklyn.

“On the Islanders’ end, they might be better off financially than at Nassau Coliseum. But under the current deal, I think they realize they’ll never be able to have the type of revenue coming in to compete with other big-market teams to sign top players.”

Three-quarters through this season, the Islanders are averaging 13,424 fans per home game, ranking 28th out of 30 NHL clubs. During their farewell tour at Nassau Coliseum last season, the club’s average attendance was 15,334.

Barclays Center seats 15,795 for hockey — including about 1,500 with obstructed views that have sold poorly despite discounted pricing.

The Islanders declined comment, but Barclays Center CEO Brett Yormark on Friday denied his arena wants out of the deal early.

“We are enjoying the first year of hockey in Brooklyn,” he told The Post. “We are looking forward to a heated playoff run and a long future and partnership with the Islanders.”

The 18,000-seat Barclays Center arena originally was retrofitted to accommodate hockey, but star architect Frank Gehry’s spectacular design was scrapped in 2009 to cut costs. Ellerbe Becket and SHoP Architects co-designed the sleek glass-and-steel, clamshell-like Barclays Center about 200,000 square feet smaller than the original Gehry design.

Wang only agreed to move the team to Brooklyn a year after Nassau County voters rejected a 2011 referendum that would have helped him fund the building of a new arena there.