Ellsbury nearly has full range of motion after suffering a partially dislocated shoulder April 13, when he was trying to break up an inning-ending double play against the Rays.
"He just looked good in the weight room, he looks good in the training room," said manager Bobby Valentine. "Now I haven't seen him in the field of dreams out there where it's all green and he looks so natural. He hasn't had any setbacks. So it's all good."
The Red Sox placed Ellsbury on the 60-day disabled list Sunday to clear room on the 40-man roster for Mauro Gomez, who was recalled from Triple-A Pawtucket to replace injured outfielder Darnell McDonald (right oblique strain). The earliest possible return for Ellsbury is now June 13, though that could be a stretch.
"We can start counting days for the best-case [scenario], but it's going to be after that," Valentine said.
Ellsbury, 28, is building his strength and working on his agility and cardio.
"He's worked really hard on those things with his legs," Valentine said. "He looks really good."
The Red Sox don't anticipate Ellsbury needing shoulder surgery. Monday's game against Seattle was the 28th contest Ellsbury missed since going on the disabled list April 14.
Marlon Byrd made his 18th start in center field Monday. Ryan Sweeney made his first three starts of the year in center field during Boston's previous four-game series with Cleveland.