Adu has not played for the national team since 2009 and is currently playing for Caykur Rizespor in the Turkish second division after a series of disappointing loan spells.
The Gold Cup features 12 teams from North and Central America and the Caribbean and the winning team qualifies for FIFA's Confederations Cup in 2013.
The tournament also offers a chance for players looking to break into the national team before qualifying begins for the 2014 World Cup and Adu now has a chance to stake his claim.
Bradley said he was simply keen to see how the 21-year-old had developed since he was last in the national team set-up almost two years ago.
"It's not that we have seen anything specific with his new club... its a package," Bradley said.
"He is a player that certainly we all know and who, at different times, has shown some special soccer abilities (although) he hasn't always been able to make them count at different levels in different situations.
"We respect that he made the move to (Turkey) to go to a smaller club to show he was willing to do whatever to keep going - we are looking forward to see how he is handling things."
Adu, who signed a contract with D.C United in Major League Soccer at the age of 14, was hyped as the biggest talent in U.S. soccer but his career went gone off the rails in Europe with failed spells at Benfica and Monaco.
There is no place in the team for Sporting Kansas City striker Teal Bunbury in a squad but New York Red Bulls' 18-year-old striker Juan Agudelo was selected after scoring twice in his four appearances for the national side so far.
The U.S. face Spain in Boston on June 4 and then open their Gold Cup Group C campaign against Canada in Detroit on June 7.
Bradley's team then face Panama in Tampa and Guadeloupe in Kansas City.
Eleven of the squad have a Gold Cup title to their name and Landon Donovan has three Gold Cup winners medals.
The last time the United States played Spain was in the 2009 Conferations Cup when Bradley's team pulled off a surprise victory and ten of the current squad featured in that game.
Squad:
Goalkeepers: Marcus Hahnemann (Wolverhampton Wanderers), Tim Howard (Everton), Nick Rimando (Real Salt Lake).
Defenders: Carlos Bocanegra (Saint-Etienne), Jonathan Bornstein (UANL Tigres), Steve Cherundolo (Hannover), Clarence Goodson (Brondby), Eric Lichaj (Leeds), Oguchi Onyewu (Twente), Tim Ream (New York Red Bulls), Jonathan Spector (West Ham United).
Midfielders: Freddy Adu (Rizespor), Michael Bradley (Aston Villa), Clint Dempsey (Fulham), Landon Donovan (Los Angeles Galaxy), Maurice Edu (Glasgow Rangers), Benny Feilhaber (New England Revolution), Jermaine Jones (Blackburn Rovers), Sacha Kljestan (Anderlecht), Robbie Rogers (Columbus Crew).
Forwards: Juan Agudelo (New York Red Bulls), Jozy Altidore (Bursaspor), Chris Wondolowski (San Jose Earthquakes).
