The Boston Red Sox aren’t the only team downplaying a potential reunion with Craig Kimbrel.

The Atlanta Braves, with whom the All-Star closer began his Major League Baseball career, are on the rise in the National League East, but general manager Alex Anthopoulos recently indicated on MLB Network Radio on SiriusXM that the club probably won’t pursue Kimbrel in free agency.

“He makes everybody a lot better,” Anthopoulos said of Kimbrel. “He’s one of the best closers of all time. I did come out early in the offseason and, not speaking specifically about him, but (said) our payroll, our model, I don’t know that us spending big, elite dollars on a reliever — length, the term and all that — I don’t know that that model works for us.”

Anthopoulos’ stance is similar to that of Red Sox president of baseball operations Dave Dombrowski, who has said several times this offseason he doesn’t anticipate Boston making a large expenditure for an elite closer.

Kimbrel certainly qualifies as an elite closer, although his market has been slow to develop. He’s finished in the top 10 in Cy Young voting in five of the last eight seasons and has recorded 333 career saves. The hard-throwing right-hander owns a 1.91 ERA, a 0.92 WHIP and 14.7 K/9 in 542 career relief appearances spanning 532 2/3 innings.

It was rumored earlier this offseason that Kimbrel was seeking a contract north of $100 million. More recent reports have indicated that Kimbrel’s asking price has dropped, but the 30-year-old still might be eyeing the five-year contracts Aroldis Chapman ($86 million) and Kenley Jansen ($80 million) signed before the 2017 season while negotiating his next payday.

Kimbrel, a seven-time All-Star, is coming off a 2018 campaign in which he posted a 2.74 ERA, a 0.995 WHIP and 13.9 K/9 in 63 regular-season appearances with the Red Sox. He struggled in the playoffs despite Boston’s World Series triumph, but his overall track record is impressive nonetheless, so it’s strange to see him seemingly generate such little interest in free agency.

Kimbrel, who spent the past three seasons with Boston, was a third-round pick of the Braves in 2008. He spent his first five seasons with Atlanta, leading the NL in saves each season from 2011 to 2014, before landing with the San Diego Padres for a year and then heading to Boston.

Thumbnail photo via Mike DiNovo/USA TODAY Sports Images