On Monday, Red Sox chairman Tom Werner said it was "extremely unlikely" Boston would re-sign the hard-throwing right-hander, according to The Boston Globe's Alex Speier.
Werner's comments align with a similar suggestion made by the team's president of baseball operations Dave Dombrowski last month.
"Craig did a great job for us, he's a Hall of Fame reliever,’’ Dombrowski explained to Bob Nightengale of USA TODAY Sports. "But we have not anticipated having a large expenditure for a closer.’’
The Red Sox have been linked to Kimbrel - who's spent the past three seasons with the organization - for much of the offseason but weren't interested in bringing him back unless his price tag dropped below the $100-million offer he was reportedly seeking.
Despite being one of baseball's most effective closers last season, Kimbrel remains unemployed with pitchers and catchers already reporting to spring camps.
Aside from the Red Sox, the seven-time All-Star has reportedly been linked to the Atlanta Braves and Philadelphia Phillies.