The Italo-Argentinian striker was omitted from Cesare Prandelli's Confederations Cup squad for indiscipline after embarking on a public spat with former Roma coach Aurelio Andreazzoli after May's Coppa Italia final defeat to Lazio.
But the 27-year-old is included alongside Under-21 stars Marco Verratti and Lorenzo Insigne for a specially organised international at the Stadio Olimpico, before which the Azzurri will be granted a private audience with Pope Francis.
AC Milan striker Mario Balotelli returns to the fold after flying home early from the Confederations Cup with a leg injury. The Azzurri would finish third in Brazil after beating Uruguay in a play-off.
Roma midfielder Alessandro Florenzi, 22, has the chance to add to his two caps while there are call-ups for defenders Lorenzo De Silvestri of Sampdoria, Andrea Ranocchia of Inter Milan and Luca Antonelli of Genoa.
The Italy squad will gather in Rome on Monday before meeting the Pope in the Vatican ahead of an evening game on August 14 at Roma and Lazio's home ground.