Although Major League Baseball and the players’ union have been negotiating a new collective-bargaining agreement because the current one expires next month, the system of qualifying offers was expected to be retained in some form. Under the current system, if a player rejects a qualifying offer and signs elsewhere, his former team receives a draft pick from his new one.

Alderson said the Mets were keen on keeping Cespedes and Walker for next season.

On Saturday, Cespedes exercised the opt-out clause in the contract he signed with the Mets last off-season, forfeiting $47.5 million and two years on his deal in the hope that he could land a more lucrative payday.

Cespedes, 31, hit .280 in 2016, with 31 home runs, 86 R.B.I. and an .884 on-base plus slugging percentage, so he may be able to earn more; he was expected to reject the qualifying offer. He was a key force for the Mets not only because he provided power and experience but also because he batted right-handed in a lineup dominated by left-handers.

Alderson has been reluctant to hand out large long-term contracts to free agents, and the Mets have had financial problems during his tenure. But Alderson said the Mets had already had one “very preliminary” conversation with Cespedes’s agent about keeping him in New York.