Montas, whose 30th birthday is March 21, spent Sept. 20 (retroactive to Sept. 17) through Oct. 6 on the 15-day IL with right shoulder inflammation.
He is "8-10 weeks behind in his offseason training," according to the report.
The Yankees acquired Montas and RHP Lou Trivino in an Aug. 1 trade with the Oakland Athletics for LHP Ken Waldichuk, LHP JP Sears, RHP Luis Medina and 2B Cooper Bowman.
Montas started eight regular-season games with the Yankees in 2022, posting a 1-3 record and 6.35 ERA (4.93 FIP).
Over his 39.2 IP, he struck out 33, walked 15, hit five and allowed six home runs.
In the playoffs, Montas made three relief appearances and allowed seven runs (all earned) on 10 hits (three homers) while striking out six and walking one over 6.2 IP.
While pitching for the A's earlier in the 2022 season, Montas started 19 games and went 4-9 with a 3.18 ERA through 104.2 IP (3.35 FIP).