BOSTON -- Nathan Eovaldi’s move to the bullpen and back to the active roster is getting closer.

The flame-throwing righty threw a bullpen session at Fenway Park on Friday, his second in three days. He might throw one more on Sunday before he is cleared to face hitters -- either in live batting practice or on a Minor League rehab assignment.

“He threw 27 pitches,” said Red Sox manager Alex Cora. “I just talked to him right now. He felt great. We’ll see what’s next.”

Eovaldi last threw a pitch for the Red Sox on April 17. After that, he underwent arthroscopic surgery to repair loose bodies in his right elbow. Initially, Eovaldi was expected to return in June, but he was slowed by biceps tendinitis.

Moving to the bullpen is helpful in two ways. The first is that it can prevent Eovaldi from having to go on a lengthy Minor League rehab assignment. The second is that Boston’s relief crew -- which struggled mightily in the weeks leading up to the All-Star break -- could really use a reinforcement.

There’s a strong chance Eovaldi will be the closer once he gets a few appearances under his belt.

If Eovaldi can help stabilize the bullpen, the Red Sox might be more likely to go after a starter than a reliever in the weeks leading up to the July 31 Trade Deadline, which is the last chance for clubs to deal for reinforcements, as there is no longer a waiver-trade window in August.

• MLB's new Trade Deadline rules explained

Quite simply, and regardless of what happens on the trade market, the Red Sox need to pitch better to improve upon their play from the first half.

“I think, from the rotation to the bullpen, we have to be better,” said Cora. “We know that. There were times there that we chased our tail the whole week, and that’s not easy to do. We talk about usage and performance and all that, but I think, as a group, we have to be better.”

Kelly reflective in return to Boston

For the first time since last October, when he helped the Red Sox win the World Series, Joe Kelly was back at Fenway Park on Friday for the Sox's series opener against the Dodgers. The hard-throwing righty signed with Los Angeles as a free agent in December.

It turns out he got his World Series ring a couple of weeks ago in a private meeting with Red Sox chairman Tom Werner, who has a home and many business interests in Southern California.

“He showed up, I think, 10 minutes before game time and I was like, 'Hey, man, what’s going on?’ He was like, ‘Here’s the ring,’ and we took a photo,” said Kelly. “He hand-delivered it to me right outside the clubhouse at home. That was cool. I’d rather have it that way than get a ring out here in front of my teammates now. So I got it and put it in my safe at home. It’s a gorgeous ring and I love it.”

Kelly -- who has recently emerged from a rough early-season slump similar to many he had with the Red Sox -- also loved his time in Boston.

“I was here for 4 1/2 years,” said Kelly. “Ups and downs, winning and losing. I think my favorite moments were from where I lived in a little area called Squantum and it’s kind of old-school. Most of the kids play outside and ride bikes and they’re playing Wiffle Ball, they’re playing basketball. My son, Knox, is now 3 1/2, but this is the only city he knew growing up.”

Cora: MLB All-Stars believe in the Red Sox

One thing Cora gathered from his two days in Cleveland as the manager for the American League in the All-Star Game presented by Mastercard is how much respect opposing players still have for the Red Sox, despite their underwhelming start to the season. Cora hopes his players will take it to heart and live up to expectations the rest of the way.

“We can play a lot better. Everybody knows it,” Cora said. “I think that was the coolest thing in the All-Star Game, how many people in that clubhouse still believe in us. They let us know how good we are. If we forgot about that, the three guys that were there for us and the coaching staff, the players reminded us of that, so that was the cool thing about the All-Star Game. They were like, ‘Your run is coming.’”

Moreland back early next week?

First baseman Mitch Moreland, who has played just one game for the Red Sox since May 25 due to a back injury and then a right quad strain, will continue his Minor League rehab assignment for Triple-A Pawtucket through the weekend.

There’s a chance Moreland could be back in the lineup when the Red Sox open a four-game series against the Blue Jays at Fenway Park on Monday.

“We’ll make a decision by Sunday or Monday morning,” said Cora.

The Red Sox have been thin at first base because Steve Pearce has also had a myriad of injuries and is now dealing with a knee ailment that could keep him out a few more weeks. Rookie Michael Chavis has been playing just about every day at first. Brock Holt can also play first, but he’s been busy at second base.

Johnson ramping back up

Lefty Brian Johnson -- out with a non-baseball medical issue -- has initiated a throwing program that included a bullpen session on Friday.

“Yeah, it was his second one. He feels good,” said Cora. “I’m glad that he’s able to do his baseball activities. Obviously, with him we have to stretch him out and probably get him multi innings, so we’ll take it slowly, but at the same time, he should be OK to go out on a rehab assignment [soon].”

The Red Sox lost Johnson just as he was starting to give them stability in their revolving fifth spot on the rotation.

Fifth starter?

Speaking of that fifth spot, who will pitch on Tuesday when that spot comes up again?

“We’ll find out Tuesday,” said Cora.