Nadal pulled out of the US Open and Laver Cup in recent months and has only taken part in one of the last seven Grand Slams because of injury and fitness struggles.
French Open and Wimbledon winner Alcaraz will be Spain's key figure as they bid to win the competition dubbed the World Cup of tennis for the first time since 2019, starting with a clash against the Netherlands.
Alcaraz inspired Team Europe to Laver Cup victory over Team World last weekend in Berlin.
US Open and Australian Open champion Sinner is part of Italy's squad for the finals, which start on November 19th.
The 23-year-old was crucial as Italy triumphed last year, beating Serbian superstar Novak Djokovic twice in one day, first in singles and then in doubles, in the semi-finals.
Italy, who face Argentina in their quarter-final clash, beat Australia in the 2023 final to win the competition for the first time since 1976.
