Mets general manager Sandy Alderson said Sunday that if the reported contract terms are correct, New York would not match the offer.
Reyes became the first Mets player to win the batting title, coming off his .337 season with a .384 on-base percentage.
With the signing, Miami is expected to move Hanley Ramirez to third base. Ramirez, a three-time All-Star starter, has never played a position other than shortstop throughout his professional career.
Securing Reyes is the second major step made by the Marlins in recent days. The team reached agreement on a three-year, $27 million contract with closer Heath Bell on Thursday night.
Bell, 34, is expected to be officially announced as a Marlin on Monday. Reyes' deal is expected to be announced Wednesday.
With Reyes in fold, the Marlins have a leadoff hitter who is a .292 career batter with a .341 on-base percentage and 370 stolen bases. If Miami chooses to go with Emilio Bonifacio in center field, and hit him second, the club would have two of the fastest players in the game at the top of its order.
The Marlins have been one of the most aggressive teams on the market since free agents were able to talk to other clubs five days after the World Series ended. In the first few days of the signing period, Reyes visited Miami and toured the team's new ballpark in the Little Havana section of town.
Along with Reyes, the Marlins are actively shopping for starting pitching. Mark Buehrle is a high priority, but the veteran left-hander is seeking a no-trade clause, which is something Miami doesn't generally do. That could hold up a possible deal.
The Marlins also are making a push for C.J. Wilson. Money isn't believed to be an issue; it is a matter of if the lefty wants to leave Texas for Miami.
In the past month, Reyes, Buehrle, Wilson and Albert Pujols each visited Miami to meet with team officials and see the new ballpark.
Reyes' deal will become the highest in franchise history, surpassing Ramirez's six-year, $70 million deal.