Tanner Scott is the most sought after reliever on the free-agent market after a dominant season split between Miami and San Diego. Jeff Chiu/Associated Press

With five weeks until pitchers and catchers report to spring training, adding a right-handed bat remains the top priority for a Red Sox team that has beefed up its pitching staff with the additions of Garrett Crochet, Walker Buehler, Patrick Sandoval, Aroldis Chapman and Justin Wilson. But another bullpen addition is also very much in play for chief baseball officer Craig Breslow.

Boston’s projected bullpen includes a back-end core of Liam Hendriks, Justin Slaten, Garrett Whitlock, Chapman and Wilson with many others (Brennan Bernardino, Michael Fulmer, Luis Guerrero, Zack Kelly, Zach Penrod, Greg Weissert and Josh Winckowski) in the mix, too. But the Red Sox appear interested in adding some more veteran certainty and one look at the free-agent market shows that they’re in luck. They made a better offer than the one-year, $5.5 million deal Chris Martin took from the Rangers, but he wanted to pitch close to his Arlington, Texas home.

The free-agent market for relievers has barely moved with few (Clay Holmes, Mike Soroka, Blake Treinen, Chapman and Martin) signing so far and a couple  (like Holmes and Soroka) signing with their new teams who plan to try them as starters. Teams that are looking for help have plenty of options to choose from.

Here are some available options for the Red Sox with notes on potential interest, if that’s confirmed:

LHP Tanner Scott: Scott is the clear prize of the free-agent relief class after a dominant season for Miami and San Diego. He’s going to get a lucrative multi-year deal with MassLive’s Sean McAdam hearing he might reach something in the four-year, $80 million range. The Red Sox are $26-27 million below the $241 million luxury tax threshold they said they were willing to exceed, so a serious run at Scott is possible. They’re one of a handful of teams that has been involved, but there’s expected to be a big-market bidding war. Calling anyone a clear frontrunner is probably premature considering the competition for him. Agents who represent free agent relievers believe the market is waiting on him to move.

RHP Jeff Hoffman: Hoffman had a stellar two seasons with Philadelphia and is probably the best righty out there. The Red Sox have stayed in touch with his camp. Like Holmes, some teams have designs on him starting. If he’s interested in that, the Red Sox probably aren’t the best fit. In a late-innings role, he’d make a lot of sense alongside Hendriks, Slaten, Whitlock and Chapman.

RHP Kirby Yates: Yates is a guy who has shown elite flashes for a long time and was dominant last year, posting a 1.17 ERA (and 2.50 FIP) in an All-Star campaign for the Rangers. The competition is going to be stiff for the soon-to-be 38-year-old gamer who will probably get two years.

RHP Carlos Estévez: The Red Sox have checked in on Estévez but haven’t been aggressors to this point. He pitched really well for the Angels and Phillies last year and was one of the best relievers moved at the deadline. The hard-throwing 32-year-old is a bit underrated and should get a multi-year deal.

David Robertson continues to be an effective reliever entering his age 40 season. He could be interested in signing with Boston to be closer to his Rhode Island home. Tony Gutierrez/Associated Press

RHP David Robertson: Robertson is always a bit of a wild card in free agency because he represents himself. He’s still going strong entering his age-40 season and would fit Boston on a one-year deal. That might appeal to him if he wants to pitch close to his Rhode Island residence (and his wife, Erin, is a Brookline native).

LHP A.J. Minter: Minter is a unique free-agent case because he has been one of the best lefty relievers in baseball in recent years but underwent season-ending hip surgery and may not be ready for Opening Day. The Red Sox are interested here, and have had multiple conversations with the longtime Brave.

RHP José Leclerc: Leclerc’s 4.32 ERA from last season is a bit inflated but he has always posted high strikeout numbers and his whiff (36%) and strikeout percentages (30.9%) were elite last year. That seems right up Red Sox manager Alex Cora’s alley. The 31-year-old would make a lot of sense if the top options go elsewhere.

RHP Andrew Kittredge: Kittredge gave the Cardinals a total of 70 2/3 strong innings last year and was as good as anyone at getting batters to chase. He’s a good fit the Red Sox have been in touch with.

RHP Tommy Kahnle: The Red Sox have tried to sign Kahnle a few times in the past and — you guessed it — they’ve checked in again, though nothing has heated up. He has plenty of big-market experience and had two strong years for the Yankees, who could use him again. It’s a good fit for the Red Sox.

RHP Paul Sewald: The arrow has been pointing down on Sewald for the last couple years in terms of run prevention and he was hurt at times in 2024. He doesn’t throw hard but limits hard contact, so the Red Sox could be interested in a different look.

RHP Jakob Junis: Junis is a swingman who had a 2.69 ERA in 67 innings split between Milwaukee and Cincinnati a year ago. Multi-inning weapons are always valuable and he’s someone the Red Sox poked around on last winter. But he doesn’t fit the roster as well as a high-octane one-inning guy right now.

RHP Kyle Finnegan: Finnegan is the rare player to make an All-Star team and be non-tendered in the same calendar year. He made 38 saves for the Nationals last season. He throws hard but doesn’t miss as many bats as he should, which could concern the Red Sox.

LHP Andrew Chafin: A veteran lefty who has pitched forever and seems to be linked to the Red Sox every year. There’s some doubt the Red Sox, with Chapman, Wilson, Bernardino and Penrod on the roster, are still looking for southpaw depth.

LHP Colin Poche: AL East experience helps here and the Red Sox could either find his reverse splits from last year (.811 OPS for lefties, .592 for righties) either intriguing or alarming. Tampa Bay non-tendered Poche in November.

Aaaaaaaaand…

RHP Kenley Jansen: The door is certainly closed on a reunion here because of the weird way things ended. But Jansen had a good couple years in Boston and wants to join a contender (maybe the Dodgers, if they’ll have him). He should get his wish.