Martinez was injured on Monday night when Tampa Bay's Jason Bartlett fouled a pitch that struck Martinez in the toe. Martinez's injury was diagnosed as a bruise.
"He's improving," said Sox manager Terry Francona. "He's able to put more weight on it. It's obviously sore. He's making progress, but we'd like to stay away from him.
"He feels better without a shoe. It's hard to figure a way to get him in there without a shoe. He can be available if something happens.''
Ellsbury reported some soreness in his left side just before Tuesday's first pitch, and was later checked out by doctors.
He hit off a tee before Wednesday's game against the Rays, but said his side "started to bark on me" during the session. A CT scan Tuesday showed inflammation.
"He's not going to play," said Francona. "We'll take the [X-rays and CT scan] that have been taken home with us and review everything. It's probably [about] how he feels, if he feels something."
Will Ellsbury need to go back on the DL? "I hope not," said Francona. "We'd like to know what it is, first. I don't know that anybody knows what's going on, and Jacoby's at the top of that list."
As for Drew, the right fielder has been hindered by hip soreness lately, so Francona decided to rest him as a precaution. "The last couple of days his hip has been bothering him, but he knew we needed him," Francona said. "We're playing on turf, so we want to [take him out] before something happens."
Francona also said that David Ortiz "has our blessing" if he elects to attend Jose Lima's funeral, which is scheduled for Thursday in New York. Asked if Ortiz would be back for Thursday night's game against the Royals in Fenway Park, Francona said, "We told him he can do what he needs to do.''
Gordon Edes is ESPNBoston.com's Red Sox reporter. He has covered the Red Sox for 12 years and has reported on baseball for 25 years. Ask a question for his next mailbag here. Information from The Associated Press was used in this report.