Although Caligiuri grew up in Germany, he has an Italian father and is, therefore, eligible to play for the Azzurri as well.
The 30-year-old trained with the Italy national team for the first time in May 2015, but did not make the final cut for the ensuing UEFA EURO 2016 qualifier against Croatia. He has not heard from the Italian Football Association since.
"I know it's only going to get more difficult with age," Caligiuri said in an exclusive interview with bundesliga.com. "Even so, the dream isn't dead yet and I've still a glimmer of hope that my performances for Schalke will put me in with a chance. I'd be delighted if the dream came true. If it doesn't, I'll do everything to be successful with Schalke in Europe."
Watch: Caligiuri's Matchday 26 wonder goal vs. Mainz
With Schalke on the brink of qualifying for next season's UEFA Champions League group stage, Caligiuri might not have long to wait. The former Freiburg and Wolfsburg man has had a big say in the Royal Blues' resurgence, chalking up six goals and nine assists in 32 Bundesliga appearances so far this term, but it's another German-Italian he believes has been the catalyst for change at a club that missed out on European qualification altogether at the end of 2016/17.
"Domenico Tedesco is an expert in managing the atmosphere within the team," Caligiuri said of Schalke's 32-year-old head coach, a runaway success in his debut Bundesliga campaign. "He's sensitive to the feelings of all the players. He knows exactly how to deal with disappointment and happiness after wins. I've come very few coaches with such a good feeling for team morale. When I played with his brother Umberto in the Freiburg amateurs, I never thought I'd be playing under [Domenico] one day. He's been fantastic for all of us."
Galvanised following the disappointment of last season's 10th-placed finish, Schalke are now in pole position to claim the runners-up spot behind record Bundesliga champions Bayern Munich. Die Knappen have a two-point cushion on third-in-the-table Borussia Dortmund, and will claim proverbial silver if they win their remaining two games against Augsburg (a) and Eintracht Frankfurt (h). Should they succeed, it would be the Ruhr district outfit's highest-placed finish in eight years.
"We're not resting on our laurels," Caligiuri affirmed. "When you're second in the standings, that's where you want to stay. That won't change, even if we secure Champions League qualification on Matchday 33. We want to win both games, and will give it our everything. With our fans behind us, you can't give anything but 100 percent. Six more points, and we'll definitely be this season's runners-up."