Sinner, ranked number two in the world, led Italy to a successful defence of their title last year in Spain, but will not be on home soil when the Final 8 takes place in Bologna from November 18-23.
"Jannik Sinner has not given his availability for 2025," Italian captain Filippo Volandri said.
"The Davis Cup is, and will remain, always his home and I am sure that Jannik will soon be part of the team again. In the meantime, I can count on a group ready to fight and give everything for the blue jersey."
Volandri's team is made up of Matteo Berrettini, Simone Bolelli, Flavio Cobolli, Lorenzo Musetti and Andrea Vavassori.
Sinner, who won the Australian Open and Wimbledon this year and reached the final of all four Grand Slams, will be in Turin a week before the Davis Cup to defend his ATP Finals title, where Alcaraz has also secured his place in the season-ending event.
Alcaraz will be bidding to earn Spain their first Davis Cup success since 2019, with Jaume Munar, Pedro Martinez, and Marcel Granollers also selected by the Spaniards.
World number three Alexander Zverev is set to make his first appearance at the Davis Cup Finals, with the 28-year-old named on the Germany team.
DAVIS CUP FINAL 8 DRAW (prefix denotes seed)
Quarter-Final 1: 1-Italy v Austria
Quarter-Final 2: 3-France v Belgium
Quarter-Final 3: Spain v 4-Czech Republic
Quarter-Final 4: Argentina v 2-Germany