They could get the lefty back soon, if his current progression is any indication.
Price will throw another bullpen session at Fenway Park on Thursday, marking the third time he has done so in five days.
The veteran, who hasn't pitched since Aug. 4 due to a cyst on his left wrist, looked sharp in Tuesday's side session.
"It went well," said Red Sox manager Alex Cora. "Very aggressive. Location was better. Threw the cutter, too. That's why we have one more tomorrow, and we'll decide what we do."
The Red Sox have an opening in the rotation for Sunday's game in San Diego, so there's a chance Price could slide into that slot.
It doesn't look like he will need a Minor League rehab appearance.
"We don't know yet," said Cora. "With him, kind of like, he did it early in the season [coming back without a rehab start]. When he went to Toronto he didn't have one and he was fine. The shape of his pitches and location, that's obviously very important. Let's wait for tomorrow for him to throw it and we'll talk about it after the game or Friday."
Calling all kids
Thursday will mark the resumption of the game between the Red Sox and Royals from Aug. 7 that was suspended in the top of the 10th inning in a 4-4 tie.
The festivities start at 1:05 p.m. ET at Fenway Park.
Kids 18 and under will be admitted free of charge. All other fans may gain admission for $5. All ticket proceeds will go to the Jimmy Fund.
There will be a special kid-friendly menu of items for $1. Additional menu items will be available at half price.
Fans who had tickets on Aug. 7 will gain automatic entry into the park and will be assured of sitting in their original seats.
Rocket back on the mound
The annual Old Time Baseball Game takes place on Thursday night at St. Peter's Field in Cambridge, and "Rocket" Roger Clemens will be the starting pitcher for one of the teams.
Admission is free, and the players will all be in old-timey flannel uniforms that represent various eras.
Clemens pitched for the Red Sox from 1984-96, winning the first three Cy Young Awards of his decorated career. The righty is 57 years old and finished his career in 2007 with 354 wins and 4,672 strikeouts.
Two years ago, Hall of Famer Pedro Martinez pitched in the Old Time Baseball Game, and knuckleballer Tim Wakefield got some action last year. Funds from the 2019 game will support Compassionate Care ALS to assist individuals living with ALS, their families and caregivers.