If Nathan Eovaldi returns to the Red Sox next season, it will be on a multiyear deal.

The righty, who pitched for Boston the last five seasons, rejected the team’s $19.65 million qualifying offer on Tuesday.

Players who accept qualifying offers are signed to their respective teams for the next season at the designated value. Joc Pederson (Giants) and former Red Sox lefty Martín Pérez (Rangers) were the only two of 14 players in MLB who accepted the qualifying offer.

The only other free agent the Sox extended a qualifying offer to was star shortstop Xander Bogaerts, but it wasn’t news when he rejected it, given that the remaining three years of the contract that he recently opted out of had a higher average annual value than the qualifying offer.

Though the Red Sox still can re-sign Bogaerts and/or Eovaldi as free agents, the club is now assured of receiving Draft-pick compensation in 2023 if they sign elsewhere.

For Eovaldi, the qualifying offer would have been a salary bump from the annual salary of $17 million he earned from the Red Sox over the last four seasons.

Eovaldi, who has often stood in as Boston’s ace over the last three seasons while Chris Sale has been injured, had some health ailments in 2022 that limited him to 20 starts. But Eovaldi and his representation believe he can do better with a multiyear deal on the open market.

The Red Sox, who have great respect for Eovaldi’s leadership and work ethic, are believed to still have interest in retaining him.

The hard-throwing righty was on the injured list from June 12 to July 15 with low back inflammation and from Aug. 23 (retroactive to Aug. 19) to Sept. 29 with right shoulder inflammation. He went 6-3 with a 3.87 ERA while walking 20 and striking out 103 in 109 1/3 innings.

Eovaldi’s velocity began to diminish from where it was June of last season. He attributed it to the injuries and not having time to build back his arm strength.

As recently as 2021, Eovaldi finished fourth in American League Cy Young Award voting. He played a huge role in Boston winning the 2018 World Series, with a tremendous October in which he moved between the rotation and the bullpen.