Keuchel's in shape and not far away from where he was at the end of last season, a source told MLB.com's Bryan Hoch, who also reported it shouldn't take the pitcher long to ramp back up.
The left-hander has been throwing simulated games every five days or so in Newport Beach, according to Erik Boland of Newsday.
Keuchel will likely sign after midnight on June 2, when teams no longer have to surrender a compensatory draft pick to acquire him. He rejected a $17.9-million qualifying offer from the Houston Astros in November and hasn't been able to secure a deal since.
New York's rotation, as is the case with a large chunk of its roster, is depleted due to injuries. The team is currently without Luis Severino (rotator cuff), James Paxton (knee), and CC Sabathia (knee). Still, the Yankees lead the American League East with a 34-18 record.
Last season, Keuchel led the majors with 211 hits allowed, but did pitch 204 2/3 innings in 34 regular-season starts. During his seven-year career, he's the owner of 76 wins and was named the American League Cy Young Award winner in 2015.