Crawford is first eligible to play on Sunday in his hometown of Houston, while the earliest Buchholz could be activated is Saturday. However, it is likely both players will be held out until the next homestand, which starts on July 4.
Crawford is recovering from a left hamstring strain.
"He jogged today," said manager Terry Francona. "He did six, 90-feet [increments], jogging about [half-speed]. He's improving. I think the day he could come off is the last day in Houston. I don't know how realistic that is. I guarantee, when you see him, he's OK. He knows that. We'll see how he does."
Because Crawford has been in the American League his entire career, his chances to play in front of his hometown have been limited. But Francona has already spoken openly about not forcing the issue for that reason.
"Of course," Francona said, "but he also was aware of that. We've had that conversation already. He's fine."
Buchholz, who has been dealing with lower back woes for a few weeks, last pitched on June 19.
"We're going to be really careful with him, obviously," Francona said. "He's improving, which is good. Not all the way, but I can tell you he's not going to pitch until we're comfortable he can go out and handle it. So we'll just continue to monitor that. He's not going to pitch in Houston. We'll see how it does when we go back off this trip, see where he's at."