Bradley swiftly became one of the bookmakers' favourites for the job at the English Premier League club following Martin O'Neill's resignation from the post on Monday.
Asked about the Villa speculation, Bradley, whose contract with the U.S Soccer Federation runs out in December, told a news conference ahead of his team's friendly with Brazil, that he would love to work in Europe.
"I have said over and over as well that I am always excited about new and different challenges. Certainly coaching in Europe at some point is something that I would love to do," he said.
"At the same time, I also consider it a challenge when you finish one (World Cup) cycle and begin the process of working on another one. From the time one World Cup ends, you begin to go through the process of assessing where you are."
Villa are owned by American Randy Lerner, and Bradley, who impressed during the World Cup where he guided his team to the second round, has previously been linked with Fulham before the London club appointed former Manchester City boss Mark Hughes.
Bradley confirmed a representative had spoken to Fulham on his behalf after Roy Hodgson left the club for Liverpool.
The American said he had yet to have a full discussion with U.S Soccer as both parties had agreed to get the Brazil friendly, to be held at the New Meadowlands stadium on Tuesday, out of the way before full talks.
"From the end of the World Cup, I have said the same thing: There would be a period when both sides would assess. I think that's normal," Bradley said.
"I had a few discussions with U.S. Soccer. This fixture date comes at a tricky time and so we agreed it was most important to get on and prepare for this date and then we would have some discussions following this game.
"That's where it stands. Other than that, there is different kinds of speculation on different days, so there is not much to be said until some more discussions take place."
