Bradley's current contract with the U.S national team runs out at the end of December and the coach had said before Tuesday's 2-0 friendly defeat to Brazil that talks with the federation had been put on hold until after that game.
A spokesman for the federation denied reports from U.K media that Bradley had quit in order to take up the position at Villa, left vacant by Martin O'Neill's decision to leave the Birmingham club.
"The reports that Bob Bradley has resigned are not true. U.S Soccer officials plan to continue discussions with Bob in the near future," Neil Buethe, the federation's senior manager of communications, told Reuters on Friday.
Prior to the Brazil game, Bradley said he would love the challenge of coaching in Europe but also said leading the U.S towards the 2014 World Cup would be a challenge.
British bookmakers made Bradley favourite for the job as soon as O'Neill resigned from the manager's position at Villa Park. Villa are owned by American Randy Lerner.
Bradley confirmed this week that he had contact with another English Premier League team, Fulham, through an intermediary, when their manager's position had been vacant last month.
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