Morton, who finished third in AL Cy Young voting in 2019, was scheduled to make $15 million next season if the Rays exercised his option. Meanwhile, Zunino was slated to make $4.5 million.
Neander adds the team will keep the door open to talk with both of them about a return.
Morton, 36, pondered retirement in the past, depending on whether his performance or health declined during the 2020 season.
"If he still wants to play next year ... we're going to try everything we can to make that happen," Neander said, according to Juan Toribio of MLB.com.
Morton posted a 3.33 ERA with a 10.9 K/9 across 42 starts with Tampa Bay after he signed a two-year, $30-million pact as a free agent in December 2018. The righty was even better during the postseason, allowing just seven earned runs across 30 innings over the last two years.