Damon took batting practice on the field on Saturday and pronounced himself ready. He made 30 tosses before Sunday's game, 20 at 40 feet and 10 at 60 feet.
General manager Brian Cashman said that the team would discuss a rehab assignment. Manager Joe Girardi noted the team's off-day on Thursday, after a three-game home set against Minnesota beginning on Monday, and said that Damon could return this week.
"The thing is, players always want to get back as soon as possible," Girardi said. "But you have to make sure a guy doesn't come back for one day, and then it bothers him again, and then you're without him for two weeks.
"I would rather be cautious, in a sense, maybe a day or two extra, as opposed to losing him for another two weeks."
Damon, who was placed on the DL on July 6, injured his shoulder on July 4, when he crashed into the left-field wall in an attempt to chase a deep fly ball hit by Boston's Kevin Youkilis.
"There's nothing more I need to do," said Damon, who is batting .319 with 50 runs and a .387 on-base percentage. "I'm going to feel it, probably, until the offseason, but it's not a situation where it's going to get worse. Some days I'll wake up and it'll be a little tight, but I'll come in here, jump in that hot tub and go."
With such significant players as starting pitcher Chien-Ming Wang and designated hitter Hideki Matsui also out with injuries, Damon recognizes why the team is waiting.
"I think they want to be extra cautious," he said. "What's hurt this team all year is injuries, and I don't think they want to see me jump back on the DL. But I actually think I'm fine.
"Unfortunately, you do have to understand where they come from on matters like this."