"First of all I think of us reaching the final. Then, if it is against Britain, that would be great," the 21-year-old said in an interview published in daily newspaper ABC, adding that winning the gold would be "a dream".
"You imagine the national anthem playing and you are there, winning a gold medal. We are very determined and I hope that this is what will happen, but we know it will be very complicated."
Spain have been drawn alongside Honduras, Japan and Morocco in Group D at the Olympics, with their first match scheduled for 26 July against the Asian side.
"The first match is always key to see what state the team is in, how we are doing after all these days training," added De Gea. "It's a match that if you lose, the feelings are strange. It is a key match that we have to win."
Spain are one of the favourites to win gold at London 2012, with the inclusion of three players from their UEFA EURO 2012 title-winning side - Juan Mata, Jordi Alba and Javi Martinez - in Luis Milla's squad boosting the team's credentials.