The Red Sox extended $19.65 million qualifying offers to free agents Xander Bogaerts and Nathan Eovaldi on Thursday, positioning the club to receive Draft compensation in the event one or both of those players sign with another team.

Players have until Nov. 15 at 4 p.m. ET to accept or decline the qualifying offer.

There is no chance Bogaerts will accept the qualifying offer, considering that the final three years of the contract he just opted out of had a higher average annual value than the qualifying offer.

Red Sox chief baseball officer Chaim Bloom has stated numerous times that finding common ground on a new contract with Bogaerts is the team’s top priority this offseason. Thursday marked the first day Bogaerts became eligible to sign with any of MLB’s 30 teams.

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The QO situation with Eovaldi is interesting, and increases the chances of him returning to the Red Sox for next season.

Players accepting a qualifying offer are locked in for a one-year, $19.65 million contract for the 2023 season.

The qualifying offer would be a bump for Eovaldi 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 might make the qualifying offer more appealing than testing his value on the open market.

The hard-throwing righty was on the injured list from June 12 until July 14 with low back inflammation and from Aug. 22 until Sept. 28 with right shoulder inflammation. He made 20 starts, going 6-3 with a 3.87 ERA while walking 20 and striking out 103 in 109 1/3 innings.

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

If Eovaldi returns, the Red Sox would love to see him return to his 2021 form, when he helped lead the club to a postseason run that ended in Game 6 of the American League Championship Series.

Considered a team leader due to his work ethic and team-first attitude, Eovaldi played a huge role in Boston winning the 2018 World Series. Eovaldi said many times last season he would like to remain with Boston.

The Red Sox did not extend qualifying offers to righty Michael Wacha or veteran designated hitter J.D. Martinez, meaning they won’t get Draft compensation should those players go elsewhere.

There had been much debate if the Sox would give a qualifying offer to Wacha or Eovaldi. Wacha had a tremendous 2022 season when healthy, going 11-2 with a 3.32 ERA. Wacha also spent two stints on the injured list, limiting him to 23 starts.

The Red Sox are still likely to stay engaged with Wacha to see if they can find common ground on a contract that could bring him back to Boston.

If Martinez had performed this past season like he did in 2018, ’19 or ’21, the Red Sox likely would have extended him a qualifying offer. But the 35-year-old’s production was greatly diminished in ’22, as he was limited to 16 homers and 62 RBIs in 596 plate appearances. The expectation within the industry is that Martinez won’t be back with Boston.