The value of the Mets and every other Major League Baseball team has increased substantially since then, with significant growth in the digital and television rights deals for the league.

The Wilpons, through a different corporate entity than the one that controls the team, also own roughly 65 percent of the regional cable network SportsNet New York, a cash cow primarily built on televising Mets games.

The team, on the other hand, now has the eighth highest payroll in baseball, according to Spotrac, which tracks player contracts in major sports. The Mets lost more than $50 million last season, according to people familiar with the team’s finances, largely because of declining attendance and about $50 million in annual payments on bonds used to finance the construction of Citi Field. The family is able to temper its losses in part with the money it makes from the television network, giving the Wilpons the flexibility to allow a potential deal to sell the team to collapse.

But Fred Wilpon and Saul Katz, his brother-in-law and the president of the Mets, are both in their 80s. Several of their children do not trust Jeff Wilpon, the longtime chief operating officer of the team, to run it responsibly. Estate and tax planning are the primary motivating factors in the current push to sell the team.

Last year, to balance the needs of the children who want to sell with those of Fred and Jeff Wilpon, who have long been involved in every facet of the franchise, the Wilpons included an unusual provision in the doomed deal with Cohen. After the sale, Fred and Jeff Wilpon would remain in their roles running the team for five years.

As the parties attempted to finalize the terms, Cohen wanted assurances he would have influence on financial matters, veto power on certain spending issues and, after combing through the team’s finances, a reduced sale price, according to two people with knowledge of the negotiations. The Wilpons stayed put, and the deal collapsed.

Now Allen & Company, the Wilpons’ longtime investment bank, is following a more standard process of vetting potential bidders and will soon allow them to review the team’s finances. Any buyer would have to be similarly vetted by M.L.B. and pass a vote of the league’s owners.