According to Variety, the engaged couple - who is estimated to be worth a combined $700 million - has teamed up with JPMorgan Chase's managing director Eric Menell, the bank's co-head of North American media investment banking, to discuss raising the capital to potentially make an official offer.
The team is currently owned by the Wilpon family, who was in discussions last December (19) to sell 80 per cent of the team - a sale which would have valued the Mets at $2.6 billion. However, the negotiations with hedge fund mogul Steve Cohen fell through when he failed to agree to the Wilpon's terms that they would continue to control the franchise for the next five years.
This condition will not be attached to the sale this time around.
The report may come as a surprise to some of Jennifer and Alex's fans - given that she's from the Bronx, the home of rival team the New York Yankees, which Alex also used to play for.
Variety added that whoever ends up buying the team will have to take on around $50 million (£40.3 million) in annual losses.
Alex previously opened up about his hope of potentially buying the Mets during an appearance on "The Tonight Show Starring Jimmy Fallon" last month.
"Here's what it is. I love New York City, number one," he explained. "A lot of people don't know this. Growing up I was a big Mets fan and with the exception of my daughter's birth, both of them, the best years of my life were 1986 and 2009, when we won."
"I will say this. If the opportunity came up, I would certainly look at it. And maybe you can buy them with me. I need a partner!."