The uncapped young Spaniard wants a chance to impress at international level following his exploits for Los Colchoneros in their Europa League-winning campaign
The former Under-21 international enjoyed a stellar campaign at the Vicente Calderon and was Atletico's most prolific forward after Radamel Falcao with 19 goals in all competitions.
Del Bosque has included Adrian in his provisional squad for the championship in Poland and Ukraine, with the final 23-man group expected to be announced on May 27.
While injured Barcelona forward David Villa has ruled himself out of selection, the 24-year-old Atletico striker still faces tough competition from the likes of Fernando Torres, Roberto Soldado, Fernando Llorente and Alvaro Negredo for an attacking berth.
"It's not known if I will be selected until the coach makes his final call," Adrian told Marca.
"Now that we are here, we will try to make things as best we can as we have been doing for our clubs, which is what has gotten us this far.
"I am dreaming of being at Euro 2012, as does everyone who is in the preliminary squad."
Defending champions Spain have been grouped with Italy, against whom they begin their campaign on June 10, Republic of Ireland and Croatia.