FORT MYERS — When it became clear that Craig Kimbrel was unlikely to re-sign with the Red Sox during the offseason, Alex Cora and Dana LeVangie each went out of their way to mention a different reliever who they were focused on in 2019.

While Ryan Brasier and Matt Barnes look like the two most logical candidates to replace Kimbrel as the closer, with Tyler Thornburg a dark horse to win the job if he can prove himself healthy, there was another name that Cora and LeVangie said we should keep an eye on for important work: Heath Hembree.

Among all the Red Sox relievers with at least 50 career innings, Hembree has the best strikeout-to-walk ratio (2.9), perhaps the most accurate indicator of a pitcher’s ability to get big outs without becoming a liability.

“You look at the innings and the strikeouts, he was probably the best in our bullpen,” Cora said Saturday. “There were a lot of strikeouts, a lot of swings and misses, a lot of weak contact. I’m looking forward for him to step up. And instead of giving us one out with traffic, probably get us more.”

Despite a career 3.46 ERA, Hembree has often been the most overlooked reliever in that ‘pen. Perhaps that’s because his journey wasn’t an easy one.

Three years ago, Hembree was fighting to stay in the big leagues after a 2015 season in which he optioned back and forth to the minor leagues so many times he could no longer hide his frustration. He had just a 3.14 ERA over 37 games across three years with the Giants and Red Sox, but couldn’t find a home in John Farrell’s bullpen.

“That’s the story of my career,” said Hembree, who was originally acquired from the Giants in the trade for Jake Peavy in 2014. “They say it’s harder to stay in the big leagues than to get there. For my case, it felt like that was very true. I feel like I had to pitch my throughout my career to earn my spot.”

Again in 2016, Hembree found himself spending time in Triple-A Pawtucket, where he dominated in 13 outings, striking out 22 while allowing just one run. Finally the Sox gave him a legitimate chance in the big league bullpen, but his usage was so inconsistent it’s something of a miracle he ended the season with a 2.65 ERA.

It wasn’t until 2017 that Hembree finally found consistency as a bridge to the set-up guys. And when Cora took over the helm in 2018, Hembree felt more relaxed.

“It was harder in the ‘16 season, maybe ‘17, but last year it was pretty cut and dry when the situations were going to be,” Hembree said. “They communicate with me well.”

For the first half of the season, Cora said Hembree was one of his most trusted relievers.

“Then he made adjustments on the rubber and actually threw the ball well towards the end too,” Cora said. “His fastball plays. It’s 97 mph up in the zone. His slider needs to get better, but at one point in the season he was my best guy when there was traffic out there.”

His mid-high-90s fastball earned him the nickname “Heater,” and when his off-speed pitches are working, he’s as tough a pitcher to face as anyone in the Sox’ bullpen.

“I feel like there’s a lot more I can do a lot better,” Hembree said. “There’s a lot of consistency I can bring to the table.

“You have moments, you have it where you think you found it for a month and a half and when you’re in it, you’re like, ‘don’t think about it, just show up and pitch.’ Then you come out of it and it’s like, ‘(expletive), I should’ve thought about it.’”

Cora says he won’t name a closer until March 28, Opening Day, when he calls on the new closer with a tight lead in the ninth. Hembree, who was a closer throughout his entire minor league career, said the wide-open competition is exciting.

“We feel like anybody could be a closer for any other team, we just had a Hall of Famer doing it for the Red Sox the last few years,” Hembree said. “For that aspect, I think we’ll be completely fine and I don’t see why you wouldn’t want the ball in the ninth.”

All the talk about the Sox’ bullpen being a weakness “motivates us,” he said.

“But I think we’re just used to it,” Hembree said. “Bullpens can be something to talk about. When you talk about the position, you got the position players, there’s not a weak spot there. Look at the names in the rotation. Then you go to the bullpen, ‘OK, a little bit smaller names, we can pick on these guys a bit.’

“But we don’t give a crap. We consider ourselves the offensive linemen of baseball. It is what it is. We have fun with it and we enjoy what we do.”