"Probably Monday," Ortiz said when asked about running. "If everything goes good, I'll come back and play [soon after]."
Because Ortiz is a designated hitter, his return might come a little quicker than if he was a position player.
"Because he's a DH, there's a little bit of wiggle room," said Red Sox manager Terry Francona. "But we still want him to move around before he gets in a game. Going from a boot to sliding probably isn't the best common sense."
Sunday was expected to be the last full day Ortiz was going to be in the walking boot.
Ortiz said Sunday morning that he didn't feel any soreness after hitting the day before.
"I'm not limping anymore," Ortiz said. "Yesterday, I hit and it doesn't bother me at all. I'm not sore or anything at all today."
At the same time, Ortiz knows he has the type of injury he can't return too soon from.
"It all depends on what the doctor says," Ortiz said. "The thing is, with that, they want me to be 100 percent because that's something, if it's not 100 percent, it can get worse -- worse than it was."
Not only were the Red Sox again without Ortiz and Kevin Youkilis (disabled list), but Jacoby Ellsbury missed his second straight game with a back contusion.
There's a chance Ellsbury will return Monday night in Texas.
"I don't know. I'm hoping," Francona said. "He's pretty sore. Again, when he's able to get in there and be comfortable to play, we'll get him back in there. Getting him back in too early doesn't do anybody any good. We'll give the medical people a chance to do their stuff and when he's ready, he'll get in there. Believe me, he wants to play. He's been playing every day."