Beckett tossed a side session on the team's off day Monday at Fenway Park and did well enough to think that he'll be able to return later this week. He played long toss again on Tuesday and is set to meet with team doctors before a final decision is made.
"He feels really good," Francona said. "In fact he said he could have pitched yesterday, which is good news. We have to come up with a starter either Thursday or Friday, so I told him, 'Whatever is in your best interest and if you think the extra day helps you even more, we'll push you back.' So that's where we're at."
Francona did not watch Beckett's side session on Monday, but said pitching coach Curt Young was pleased, as was Beckett.
Meanwhile, Francona indicated that pitcher Erik Bedard (knee and lat) could throw a bullpen session Tuesday at Fenway Park, and he could be ready to pitch on Monday.
"If he throws today, we're going to have to see where it goes because we don't know," Francona said. "We know we have a doubleheader coming up next Monday and we need to fill two spots. He may be a candidate or he may not. We'll see."
Also, fellow pitcher Clay Buchholz (back) played catch again on Tuesday and could be in line to throw a session off a mound later this week.
"That will be determined after we see how he bounces back tomorrow," Francona said. "When he gets to this effort level we want to see how he bounces back, but he's getting himself toward a bullpen for sure."
Joe McDonald covers the Red Sox for ESPNBoston.com.