Lorenzo Musetti and Flavio Cobolli, eighth and 22nd in the world respectively, will be the highest-ranked singles players on show for Italy, who face Austria in their quarter-final.
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.”