Bradley's contract runs out in December and when asked whether he wanted to be in charge for the next four year cycle, he said:
"At this moment there have been no conversations and there is always a process with any situation where both sides probably need time and you go from there.
"The only real comment I would make is that, I always enjoy new challenges but I also from day one have said and consider it a tremendous honour to coach the national team," he told a news conference.
Bradley, who began his coaching career at college level, coached several teams in U.S. Major League Soccer before taking on the U.S. job after their elimination at the group stage in the 2006 World Cup.
Asked whether he would be interested in a possible future in club football overseas, Bradley said he had an open mind.
"I've always enjoyed new challenges. I encourage (that) whether it is players, or actually my children, or when I coached in college, then the kids in college. I believe that is what life is all about.
"I have enjoyed the opportunities that I have had along the way, the different challenges and so as I move forward, there will always be an open mind in that regard," he said.
Bradley's son Michael plays for Borussia Moenchengladbach in Germany's Bundesliga.
The U.S topped Group C after drawing with England and Slovenia and beating Algeria and their coach said they felt disappointed having envisioned the chance of going far in the competition.
"There is a pretty empty feeling right now because I think coming out of the first round, we felt that there was a chance of doing something bigger," he said.
"I think that we responded well in each case in those three (group) games, we felt that we were improving game by game and the opportunity to take that further was there.
"We talked about that but we also talked about how it had to be done 90 minutes at a time. So at the end of it all that leaves us a little bit empty," he said.
Bradley became emotional when taking the rare step of answering a question about his son, who was arguably the best performer for the U.S at the tournament.
"He gives everything he has in every game. His commitment to try to do whatever is needed in the game to help his team is pretty clear," said Bradley, who normally avoids praising his son to the media.
