Brooklyn’s Barclays Center is pressuring the New York Islanders to sign a new lease that will eventually have them play a majority of their home games at the Nassau Coliseum while their Belmont arena is being built, The Post has learned.

If the team doesn’t agree to a new lease, Barclays will opt out of the lease after the 2018-19 season, possibly leaving the Islanders homeless, a source said.

The Islanders have already agreed to play up to a third of their home games at the much smaller Coliseum — but that offer doesn’t seem to be enough for the executives at Barclays, sources said.

Barclays loses money on each Islanders home game and would like to negotiate a new short-term lease, perhaps for three years, that would relieve some of that financial burden, sources said.

Under the Barclays proposal, three sources close to the situation said, the Islanders would play a dozen or so games at the Coliseum next season and then ramp up that number to more than 21 by the 2020-21 season.

For the Islanders, they need a home arena for the next three seasons. The Belmont arena will not be ready until the 2021-22 season, at the earliest.

Both Barclays and the Islanders have only until Jan. 31 to opt out of the 25-year lease signed in 2012 — and work out a new deal.

The drama surrounding the team’s fate is amping up because the 13,900-seat renovated Coliseum is not yet NHL-ready. Just recently, league boss Gary Bettman toured the suburban building and changed his tune — saying he would allow some Islanders games to be played at the Coliseum, which has but a few corporate suites.

Gov. Cuomo is pressuring both sides to agree to a new three- or four-year lease in the next week — one that would include an unspecified number of games played at the Coliseum, sources said.

The Islanders played at the Coliseum from 1972 to 2015, before moving to Brooklyn. Although it started out with high hopes, the Barclays-Islanders relationship has not worked for either side.

Barclays pays the Islanders a guaranteed $55 million and collects revenue from games, sponsorships and suite sales. Last year, Barclays lost $6 million on the Islanders, public records show.

The Islanders home has poor ice conditions and a made-for-basketball design that makes one goal obscured from some seats. The team’s average attendance of 12,059 this season ranks last in the NHL.

Barclays is pushing for games at the Coliseum because Barclays, in winning the right to manage the building, promised local officials a professional hockey team would play there.

But no professional hockey team now plays there.

Barclays owner Mikhail Prokhorov — who also owns the Brooklyn Nets and the Nassau Events Center, which now manages the Uniondale arena — could be in default of his Nassau County deal should the Islanders not play enough games there.

Brooklyn Sports & Entertainment CEO Brett Yormark is leading negotiations for Barclays and Oak View Group CEO Tim Leiweke, a co-investor in the proposed Belmont arena, is handling them for the Isles, sources said.

Both sides are still negotiating and the number of games the Islanders will play in the Coliseum is not yet set, sources said.

Barclays and the Islanders declined comment.