With Edwin van der Sar retiring, Red Devils are on the hunt for a new No.1 and are believed to have tied up a deal for the Spanish starlet to join them this summer
Reports continue to suggest that Atletico Madrid had agreed an £18 million fee with Manchester United for the Spanish goalkeeper.
United are on the hunt for Edwin van der Sar's successor and have admitted the 20-year-old star is the man they want to bring to Old Trafford, but De Gea is keen to focus on the his duties at the tournament in Denmark before deciding his future.
He told Sky Sports: "I will only speak about my future after the end of the Euro Under-21s.
"Right now my challenge is to help the Spain team, but generally my desire is to play at the top and to improve day to day."
At the end of May, United seemed to confirm a move had been completed for the young goalkeeper, but De Gea's lawyers eventually denied a deal had been completed.
De Gea has become a regular at the Vicente Calderon and played all 38 matches last season in La Liga, having won the Europa League with the Atleti in the previous campaign.