Houston made an offer to McCullers recently, Jon Heyman of MLB Network reported Tuesday.
A source described the Astros' offer to Rome as "strong." However, a deal isn't yet in place.
The 27-year-old, who has spent his entire career with the Astros, is scheduled to become a free agent after this season. He avoided arbitration in January by agreeing to a one-year, $6.5-million contract.
After missing the 2019 season while recovering from Tommy John surgery, McCullers posted strong numbers during the shortened 2020 campaign. In 11 starts for Houston, he went 3-3 with a 3.93 ERA, 3.70 FIP, and 1.16 WHIP with 56 strikeouts.