"I'd say it's questionable for him to throw tomorrow, which would then make it questionable that he would start in his next start, which means that he won't make it more than likely if he doesn't throw today or tomorrow," Valentine said before Thursday's game against Minnesota.
Beckett had back spasms in his last outing Tuesday against Detroit. He left the game in the third inning with the bases loaded and two outs.
"He feels much improved today, had a great night's sleep. Still a little limited in his motion," Valentine said.
Valentine is undecided on if Beckett will require a stint on the disabled list.
"I'm going to talk to Josh," Valentine said. "He's been through this a couple times before. I'll just get all the information, figure out if Tuesday is feasible or Wednesday is feasible, what that does for the rest of the staff, and if it would be better to give him the entire [15-day] break."
Beckett went on the DL once this year and missed 16 games in June with right shoulder inflammation. He's 5-9 with a 4.54 ERA in 18 starts. The Red Sox are 7-11 when he takes the mound.
Valentine would not say who would fill Beckett's place Sunday if the right-hander can't pitch. Franklin Morales is the likely option and Valentine said Wednesday the lefty was "waiting in the wings" to join the rotation. Morales, currently in the bullpen, went 2-1 with a 3.42 ERA in five starts earlier this season.