The team has also agreed to a one-year deal for backup catcher Ronny Paulino, according to the same source, though both players must pass physicals before the deals can be completed.
The Mets have not officially announced either signing.
Carrasco, 33, posted a 3.68 ERA in 63 games split between the Pirates and D-backs last season, striking out 65 batters in 78 1/3 innings. Though he has produced a 4.31 ERA in a six-year career that also included stops in Kansas City and Chicago, Carrasco has improved his ERA for five consecutive seasons.
Having already lost the majority of their bullpen members to free agency, the Mets remain in need of capable arms to slot in front of closer Francisco Rodriguez and setup man Bobby Parnell. One club official expressed optimism Sunday that both Ryota Igarashi and Oliver Perez will win back jobs in the big league bullpen. But beyond those four, the Mets have little of substance.
Though the Mets are wary of giving out multi-year deals this season, they were willing to do so in the case of Carrasco, whose contract is reportedly worth $2.5 million.
"Rather than falling back on a second or third choice at this point, it may be better for us to be somewhat flexible on terms," general manager Sandy Alderson said Tuesday evening.
Paulino, 29, is expected to back up Josh Thole behind the plate, in an effort to see if Thole can be a viable everyday catcher in the big leagues. After batting .259 in 91 games last year for the Marlins, Paulino still has eight games remaining on a 50-game suspension resulting from his positive test for a performance-enhancing substance.
A .273 career hitter over four seasons in Pittsburgh and two in Miami, Paulino will reportedly make $1.3 million on his one-year deal.