The new controlling owners of the Islanders have had conversations with the Wilpon family, majority owners of the Mets, about building an arena for the hockey team next to Citi Field, two people familiar with the situation said.

The news — first reported by Bloomberg earlier Thursday — comes just one week after Islanders co-owner Jon Ledecky said he is committed to keeping the team in Brooklyn long-term after an admittedly rocky first year at Barclays Center.

Ledecky and partner Scott Malkin took over a controlling interest in the Islanders from Charles Wang on July 1.

A spokesman for the Mets and Sterling Equities, the Wilpons’ real estate company, declined to comment.

Multiple sources have said the Islanders and Brooklyn’s Barclays Center both have the ability to opt out of their 25-year license agreement. While it’s not clear when the sides would have to make a decision about exercising the clause, the sources have said that the opt-outs could trigger the Islanders’ exit after the fourth year.

An Islanders spokesman said the team “will not comment on rumors and speculation.”

Barclays Center spokesman Barry Baum said, “Last week Jon Ledecky told the media and later fans at a town hall event that ‘Barclays is our home.’ If you have any further questions, please call Islanders’ ownership.”

Ledecky said last week that he is committed to the Barclays Center as the Islanders’ long-term home, but he expects the arena to make improvements.

“There were challenges last year,” he said. “I would be lying to you if I said there wasn’t. Does that mean you blow up Barclays Center and leave? No. You try to improve the home you have.”

Ledecky cited players’ complaints about the ice and fans’ criticisms about the atmosphere at the arena as areas that need improvement. Ledecky said he wanted the arena to look and feel more like the home of the Islanders, which he didn’t think was the case early in the season.