Bradley's name has been on a list of possible candidates to take over since Martin O'Neill quit days before the start of the Premier League season.
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"I would love to have a discussion and hear more," the 52-year-old American said in an interview with Sky Sports News.
Bradley, who steered the U.S. to the second round at the World Cup finals in South Africa, said he was keen to test himself in the Premier League, calling it the best league in the world.
"The possibility of working in the Premier League at some point would be a goal for sure," he said.
However, he said there had been no contact from Villa or the club's American owner Randy Lerner.
"Everyone knows that for the moment Kevin MacDonald is the caretaker manager and the first step is for a decision to be made with him. He's a good man," Bradley said.
"As a manager the first thing you always want to have is respect for other managers.
"I know the reputation Kevin MacDonald has within the club and first things first, (there needs to be a) decision in terms of his future.
"Aston Villa is a tremendous club. They have such a strong following, so that would be a club that I think anyone would have an interest in."
MacDonald, thrust into the Villa Park hot seat, began with a 3-0 defeat of West Ham United and a 1-1 draw with Rapid Vienna in the Europa League but Villa suffered a 6-0 hammering by promoted Newcastle United on Sunday.
Bradley, whose son Michael plays in Germany with Borussia Moenchengladbach, has never coached outside the U.S.
"I feel I have the ability to work in Europe and it's something I'd like to do in my career," he said. "I'm excited about that possibility whenever it comes and wherever it comes."
No American has ever managed in the top flight of English football.
