The investigation follows claims made by a former official of the Cyprus FA, Spyros Marangos, that he has evidence that certain members of the UEFA executive took inducements when the vote was made in 2007.
In a statement, the DNA did not name who they were investigating but Mircea Sandu is the only Romanian on the UEFA executive and was a member at the time of the vote.
Later in Nicosia, Marangos said at a news conference on Friday that he was waiting for Cypriot police to invite him to provide the information he had.
He added that he would only be prepared to go to court in Cyprus. "We are on EU soil," he said. "Our court is European. Let them (UEFA) come here."
He added: "The aim is for the truth to come to light."
Local media in Romania named Sandu on Friday and he denied the allegations.
'INVESTIGATING CLAIMS'
The DNA statement said it was acting following reports in the international media.
"Anti-corruption prosecutors are investigating claims regarding alleged corruption in that certain members of the UEFA executive committee might have favoured the two states," the DNA said.
Sandu, 58, who has been head of the Romanian FA since 1990 and became a UEFA executive member in January 2007, two months before the 2012 decision was taken, said he had no part in any corruption.
"There is no proof that any UEFA official has taken a bribe. I cannot be accused because there is no poof and no reason," Sandu told private television station Realitatea TV.
"The respective Cypriot has neither offered any names nor has he shown any proof, and no corruption has taken place."
UEFA has begun legal action against Marangos - a former board member of the Cyprus FA - who said he had evidence of corruption relating to the decision to award Poland and Ukraine the Euro 2012 championship.
Germany's respected Suddeutsche Zeitung newspaper reported that Marangos had said he had evidence that certain UEFA representatives were corrupted in the bidding process in 2007, when Italy and a joint Croatia/Hungary bid missed out.
Bid processes for soccer tournaments have recently come under scrutiny with world governing body FIFA provisionally suspending two members of its executive committee on suspicion of selling their votes to host the 2018 and 2022 World Cups.
Polish and Ukrainian officials have dismissed any allegations of wrongdoing, the former describing Marangos' accusations as slander.
