David Butler II-USA TODAY Sports

Red Sox starter Nathan Eovaldi threw a four-inning simulated game at Fenway Park on Sunday morning. The right-hander faced the likes of Abraham Almonte, Tommy Pham, and Trevor Story while throwing approximately 65 pitches.

“It felt good,” Eovaldi told reporters (including MassLive.com’s Christopher Smith) prior to Sunday’s 13-3 win over the Royals. “I was trying to use all my pitches. It’s a little tough to get going early in the morning. But I felt like I was finishing my pitches for the most part and I mixed them all up.”

Eovaldi, who last pitched for the Red Sox on August 12, has been on the 15-day injured list with right shoulder inflammation since Aug. 19. If the 32-year-old wakes up on Monday morning with no complications, he could be in line to make a rehab start for Triple-A Worcester at Polar Park later this week.

“He looked good,” manager Alex Cora said. “Now we’ll see how he feels tomorrow. He mixed everything up. A lot of splits and the slider and the curveball. The quality of the fastball was OK. So now it’s just a matter of how he reacts to it and what’s the next step. Obviously we’re running out of time as far as games and all that stuff. So we’ll see what’s next.”

As noted by MLB.com’s Ian Browne, Eovaldi would be on track to make two more starts with Boston before the end of the season if he rehabs with the WooSox on Friday. The veteran hurler has been limited to just 18 starts this year due to two lengthy stints on the injured list.

“I’d love to pitch in front of the home crowd again,” said Eovaldi, who is eligible for free agency this winter and has yet to discuss a contract extension with the Red Sox despite wanting to return to Boston.

Story, meanwhile, has been sidelined since last Sunday, when he banged his left heel on the first-base bag in the seventh inning of a 1-0 win over the Orioles in Baltimore.

Cora was initially optimistic that Story would be back for this weekend’s series against the Royals, but that did not happen as expected. Still, the 29-year-old second baseman took an important step forward on Sunday by facing off against Eovaldi as well as running the bases.

Depending on how he feels over the next two days, Story could return to the Red Sox lineup for Tuesday’s series opener against the Reds in Cincinnati.

“With Trevor, it’s about running right now,” Cora said. “He ran the bases today. We’ll see how he feels tomorrow. I’ve been saying this for a few days: the goal is for him to play the next day. So we just have to be patient with it.”

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