Pedroia will stay under the supervision of Williams for the rest of the week as he tries to work out the inflammation in his left knee that occurred after he played in just three games following surgery.
It was Williams who performed cartilage restoration procedures on Pedroia and Wright in 2017.
"[Wright's] on his way back so we should know a little bit more about what's going on with him," Red Sox manager Alex Cora said before Monday's game vs. the Nationals. "Everything points out that he should be fine. Actually, yesterday, he threw a short bullpen in New York, so things are trending in the right direction."
Wright has performed well for the Red Sox in relief and as a starter this season, going 2-1 with a 3.38 ERA in 10 appearances. His role when he comes back could depend on how Drew Pomeranz fares in his Minor League rehab assignment, which starts with three to four innings Monday night in Pawtucket.
With Pedroia, the Red Sox are exercising patience with the hope he can stay healthy when he does come back.
"We don't know [a timetable] and one thing for sure, like we said in Spring Training, when he's ready, he's ready. We're not going to put a timetable for this," said Cora. "The fact that he's there with the doctor and the doctor can see everything that he can do and they can identify what he can do or cannot do or what we should do as far as treatment, I think it's great. Dustin, he's OK with it to spend time there and see what's going on, which is great."
J.D. to play Tuesday, Wednesday
Cora chose Monday's series opener against Nats ace Max Scherzer as the night to keep star slugger J.D. Martinez out of the lineup, as the Red Sox play without the DH.
Martinez will be back in there against righties Tanner Roark and Erick Fedde on Tuesday and Wednesday. The Red Sox don't play Thursday and will be back under American League rules this weekend in Kansas City.
Martinez actually has a decent career track record against Scherzer, his former teammate in Detroit, going 2-for-7 with two homers against the righty.
"Just talking to him, he didn't want to have two off-days in a row, Wednesday and Thursday, so he'll play those two [Tuesday and Wednesday]," said Cora.
Thornburg on track for activation
Reliever Tyler Thornburg is expected to come off the disabled list either Tuesday or Wednesday, marking the first time he will be on the active roster for the Red Sox since his acquisition from the Brewers in December of 2016.
Thornburg underwent a procedure to repair thoracic outlet syndrome on his right shoulder last season.
He was sharp in the last two appearances of his Minor League rehab assignment, and the Red Sox think he is at last good to go.
"Yeah, he bounced back great, just a matter as to how he feels today as far as playing catch," said Cora. "And obviously he pitched Saturday. We feel pretty good where he's at right now."