Switzerland were held 1-1 by Wales in their Group A opener in Baku and on Wednesday take on Italy who beat Turkey 3-0 in Rome.
"I can't wait to play this match, I can't wait to see Roberto again tomorrow. He's a great man, an excellent coach," said Liverpool player Shaqiri, who had a brief spell at Inter six years ago.
"Italy are an excellent team, among the favourites. The team are very balanced, between attacking and defending. They're a great team who play well together, there are no great players of the past like (Andrea) Pirlo, but Mancini has done a great job. Italy are so successful because of this. They have grown as a team."
The Swiss come up against an Italy side who have not conceded a goal in a nine-match winning streak. But Shaqiri knows Italy will be a force to be reckoned with going forward, after they scored more than twice in a European Championship finals game for the first time against Turkey.
"I imagine that Italy will attack. It's not the Italy who had the tendency to defend," added Shaqiri. "The current one are spectacular, they play very attacking football and they feel comfortable playing like that."
Swiss coach Vladimir Petkovic returns to the Stadio Olimpico where he coached Lazio for two years until 2014 before taking over the national side.
"(Italy) are a big favourite, not only in this game, but also for the tournament," said the 57-year-old. "But we must show our qualities, we must surprise, amaze Italy. We have shown against big opponents that we can score."
Mancini, meanwhile rated Shaqiri as "one of the best attacking midfielders in Europe".