The 52-year-old Bradley, who has a contract to coach the U.S. national team until the end of the year, says his representatives have held talks with Aston Villa, which has been without a manager since Martin O'Neill's surprise departure on Aug. 9.
"I think Aston Villa is a massive club with great history and a great following, and those type of opportunities would of course be of interest," Bradley told BBC Radio.
Kevin MacDonald has taken temporary charge of Villa since O'Neill left, reportedly because of disagreements with Lerner over transfer policy.
Bradley, who guided the U.S. to the last 16 in the World Cup this summer, is one of a number of coaches to have been linked to the vacancy at Villa Park and said he had ambitions of coaching in Europe.
"I've always been excited about being a manager in Europe, but at the same time I'm proud of the work we've done with the U.S. team over the last four years," Bradley said. "It is important to consider that as a challenge as well. So we'll see what happens.
"There have been discussions with some of my representatives to at least find out the situation, but Aston Villa seem to have taken a good stance where they have been patient. I would certainly be honored to have that conversation (with Lerner)."