"We haven't zeroed in on anyone yet, but that sixth man is probably going to happen," Lovullo said.
Adding another starter will protect rookie hurlers Henry Owens and Eduardo Rodriguez, who are approaching their innings limits.
The team will stay in line with its rotation through Wednesday. Rick Porcello will get the nod Monday, followed by Owens on Tuesday and Joe Kelly on Wednesday. The team has an off-day on Thursday.
Steven Wright, who is still dealing with side effects from a concussion, is unlikely to be a candidate. The knuckleballer has been on the disabled list since getting hit in the head by a fly ball during batting practice on Aug. 14.
"Concussions are a really ticklish issue. Steven is doing a really good job of following the program, but we don't have a cookbook here on how to follow it," Lovullo said. "We just have to get the feedback and keep moving forward."
A decision on Wright's progression will come after he's re-evaluated Tuesday.
Right-hander Matt Barnes, who's experienced minor elbow discomfort of late, may also be unavailable.
• Pablo Sandoval was out of the lineup for Saturday's game against the Phillies. He's day to day after being scratched from Friday's game due to mid-back tightness.
• Mookie Betts has been taking reps in right field the last few days and could see time at the position in the coming days. Lovullo said that decision will be rediscussed Sunday.
• Infielder Deven Marrero was recalled from Triple-A Pawtucket on Saturday. It marks his third stint with the club this season.
Quinn Roberts is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.