McClean, 23, who had not played an English Premier League game when Ireland beat Estonia in November to reach their first major finals in a decade, has been instrumental in Sunderland's recent climb up the table.
The Northern Ireland-born player was given a standing ovation after making his international debut in a friendly against Czech Republic in Dublin in February.
"He's young, he's physically strong and he's improved... I think he can give us energy," Trapattoni told a news conference.
McClean is unlikely to start ahead of first-choice wingers Damien Duff and Aiden McGeady but could make an impact off the bench at next month's tournament.
Trapattoni's squad will lean heavily on the experienced trio of captain Robbie Keane, goalkeeper Shay Given and defender Richard Dunne.
All three, together with Duff, featured in Ireland's last major championship appearance 10 years ago when Spain knocked them out of the World Cup in the round of 16.
"We will look to emulate the attitude and performance that brought us qualification," said Trapattoni.
Defenders: John O'Shea (Sunderland), Richard Dunne (Aston Villa), Sean St Ledger (Leicester City), Stephen Ward (Wolverhampton Wanderers), Kevin Foley (Wolverhampton Wanderers), Stephen Kelly (Fulham), Darren O'Dea (Celtic).
