Discussions between the sides reportedly started to gain steam Tuesday.
McCullers, who has spent his entire career with the Astros, was scheduled to become a free agent after this season. He and the team avoided arbitration in January by agreeing to a one-year, $6.5-million deal for 2021.
McCullers had a solid comeback season in 2020, posting a 3.93 ERA, 3.70 FIP, and 1.16 WHIP with 56 strikeouts across 11 regular-season starts after missing all of 2019 recovering from Tommy John surgery.
The 27-year-old owns a lifetime 3.70 ERA and 1.26 WHIP with 565 strikeouts across 508 2/3 innings. An All-Star and World Series champion in 2017, he's been an important member of the Astros' rotation when healthy but hasn't always been durable; McCullers has never made more than 25 appearances or thrown more than 128 1/3 innings over a 162-game season.
McCullers looks set to become a pillar of a Houston rotation that's beginning to transition away from veterans Zack Greinke and Justin Verlander.