FORT MYERS, Fla. — Manager Alex Cora said Monday that the Red Sox are “still engaged” in the free-agent market with interest in position players and pitchers.

“We’re trying to improve. And if there’s an opportunity to do that, I bet we’ll jump on it,” Cora said.

The Red Sox are left-handed hitter heavy so could be in the market to add a right-handed hitter. Boston had interest in Gio Urshela, but he agreed to a one-year, $1.5 million deal with the Tigers on Friday. Right-handed hitters who remain unsigned include Adam Duvall, Tommy Pham, Michael A. Taylor, Donovan Solano and C.J. Cron.

Romy Gonzalez, a 27-year-old infielder and outfielder, is one of the internal options on the 40-man roster fighting for a spot. As the Red Sox survey the market, Gonzalez is confident he can fill that role.

“Obviously a goal of mine is definitely to break with the team and help in any way I can,” Gonzalez said. “When I’m healthy I feel like I’m just as good as anybody. I’m very confident in my ability. I’m very excited just for the opportunity to be there.”

Boston claimed Gonzalez off waivers from the White Sox on Jan. 31. He played in 86 major league games for the White Sox from 2021-23, making 46 starts at second base, seven in right field, four at shortstop, three at third base and three in left field.

He has minor league options remaining so the Red Sox can option him to Triple-A Worcester.

“I bring a certain level of athleticism to the diamond, especially on the base paths,” he said. “I love running the bases, creating chaos. And obviously defensive versatility – I’m very comfortable anywhere you put me.”

Gonzalez has a hit .258 in 286 games (1,186 plate appearances) in the minors. He has a .222 average in 239 plate appearances in the big leagues. He belted 24 homers in 93 games between Double A and Triple A in 2021.

“I’m a bigger guy,” he said. “I like to get my hands extended and drive the ball to the gaps.

“I’m really honing in on cutting down the swings-and-misses and chasing outside of the zone,” he added. “Last year was kind of a tricky year. I tore my labrum in my bicep the second week of the season. I was grinding through that for a bit. So I feel like I had to cheat to get to pitches. But this year I’m feeling as healthy as ever.”

Gonzalez said he was “extremely excited” when the Red Sox claimed him because he would have the chance to play for Cora, a fellow University of Miami alum.

KUTTER CRAWFORD pitched two innings, allowing one run on three hits, with a strikeout in Boston’s 3-3 tie with the St. Louis Cardinals on Tuesday in Jupiter, Florida.

Nick Sogard, who played 60 games for the Portland Sea Dogs in 2022, hit a two-run home run and had a sacrifice fly for Boston. Chase Meidroth, who hit .255 in 91 games with Portland last summer, added two hits.

BRENNAN BERNARDINO went from being an April 2023 waiver claim to the Red Sox’ best left-handed reliever last year.

The Boston chapter of the Baseball Writers’ Association of America presented him with the Red Sox’ 2023 unsung hero award. He posted a 3.20 ERA in 55 outings (50 2/3 innings), including six starts as an “opener.”

Bernardino, who turned 32 in January, averaged 10.3 strikeouts and 3.2 walks per nine innings.

With the encouragement of Red Sox game plan coordinator Jason Varitek and others, he has one more weapon in his pitch mix this season.

“Everything I can do better,” Bernardino said Tuesday. “I got a new pitch that I’ve been working on, the cutter. That’s a pitch I think is really going to help me against righties.”

Bernardino struggle at times against righties last year. He held left-handed hitters to a .169 batting average but right-handed hitters batted .304.

“It (cutter) was something we talked about at the end of the year last year,” Bernardino said. “I talked with Tek about it. And then once (new pitching coach Andrew) Bailey came in here, it just assured that’s the pitch we needed to attack.”

Varitek downplayed his involvement, saying he simply encouraged Bernardino.

“I don’t know if I was one of the ones,” Varitek said. “I think that came from our pitching department before me and I’m encouraging what they came up with. I saw him throw it for the first time the other day. It looked good. It looked good and it’s a piece to add to his repertoire. Still a work in progress.”

Devin Rose, a clubhouse analyst of major league strategic information, worked on finding a comfortable cutter grip for the lefty.

“I’m ready to go,” Bernardino said. “I’m not going to get better with it unless I use it. So I’ve got to use it. Spring training is a good time for trial and error.”

Bernardino mainly threw a two-seam fastball and curveball last year. Opponents batted .238 with a .188 expected batting average against his curveball.

THE RED SOX have signed Jason Alexander – the right-handed pitcher, not the actor who portrayed George Costanza in Seinfeld – to a minor league contract and assigned him to Triple-A Worcester, according to the team’s transactions log. Alexander will head to minor league camp in Fort Myers.

Alexander is 30 years old and made 18 appearances (11 starts) for the Brewers in the majors two years ago. In 2022, Alexander went 2-3 with a 5.40 ERA in 71 2/3 innings. In 2023, he split time between three levels of Milwaukee’s system, posting a 6.14 ERA in 63 innings. The former undrafted free agent was with the Angels and Marlins organizations before joining the Brewers in Nov. 2021, then hit minor league free agency again at the end of last season.