Arroyo, who'll be 37 at the beginning of spring training, is seeking a three-year deal, according to a source, but he may accept a two-year offer with a vesting option for 2016.
The largest contract Alderson has ever given a free agent in four offseasons with the Mets is two years, $12 million to Frank Francisco.
The Mets are reported to be in the market for pitching with Matt Harvey scheduled to miss next season after having Tommy John surgery.
The Mets recently had dinner with Jay-Z regarding his prized client, Robinson Cano, but they don't appear to be serious contenders to sign the second baseman.
Arroyo went 14-12 with a 3.79 ERA in 202 innings for the Reds in 2013, and he is 138-127 with a 4.19 ERA in his career.
Arroyo has pitched the third-most innings in the majors since 2005 (1,895 2/3) behind CC Sabathia (1,999 1/3) and Dan Haren (1,927 2/3).CORCORAN: Twins sign Ricky Nolasco to four-year, $49-million deal