Obama, who has vowed not to identify his running mate until his supporters have been alerted via email and text message, declined to say whether he has informed the potential running mate of his decision.
"I won't comment on anything else until I introduce our running mate to the world," he told the newspaper. "That's all you're going to get out of me."
Pressed by reporters on the question at a campaign stop in Emporia, Virginia, Obama repeated that point.
"I did say that I've made the selection and that's all you're going to get," he said.
The presumptive Democratic nominee told USA Today his decision had been a difficult one, because "[w]e had some great choices."
Obama has said he wanted a running mate who is prepared to be president and "who can push against my preconceived notions and challenge me so we have got a robust debate in the White House."