"For me England are one of my favourites for the title at the Championship because they have a new, young and exciting generation of players who are very good," Shaqiri told the Stoke website (www.stokecityfc.com).
"They are a very talented group and I really think they can have a really good tournament, and even go on to win the title."
England beat 10-man Portugal 1-0 in their final Euro 2016 warm-up game at Wembley on Thursday, following wins over Australia and Turkey. They open their Group B campaign against Russia on June 11.
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Wales and Slovakia are the other teams in the group.
Shaqiri, who plays for Switzerland, has scored 17 goals in 52 games for his country and was named in coach Vladimir Petkovic's squad for the 24-team tournament, where they face hosts France, Albania and Romania in Group A.
(Reporting by Ian Rodricks in Bengaluru, editing by Ed Osmond)
