Bradley, whose contract expires in December, was non-committal on Sunday when asked if he wanted to stay in charge for another four years and Gulati also notably did not say he wanted the coach to stay on.
"We will sit down and talk. If we were carrying a trophy home it would be easy but it is not that situation," Gulati told reporters, adding that he thought Bradley "has done a very good job".
But the U.S Soccer chief said he was not aware if Bradley actually wanted to continue in the role.
"He may want a different challenge - I don't know," said Gulati, who was confident that the job would be an attractive one if it became vacant.
However Gulati, who did not rule out a future move for a foreign coach, said there would be no discussions with potential replacements before a decision was made over Bradley.
"It is not my plan to talk with people before we talk to Bob - that is the appropriate way," he said.
"Bob is our coach and he is our coach through to the end of the year," he said, before adding that "I am not saying that I will wait six months to make a decision".
"I've known Bob for a very long time and I have a lot of faith in him, I think the world of him at a personal level and we will make the right decision for the sport - it won't be about the personal level for either me or him," he said.
"It is not going to be a snap decision, I want to hear his thoughts about how things went. I have got some questions..about decisions that he made along the way. I am sure he is going to want to know about some of my reactions," he said.
Clearly pleased with the boost the World Cup had given to football in the United States, Gulati was less enthusiastic about the results gained by Bradley's team.
"Mixed results is the best way to put it and very much mixed emotions.
"I think we helped re-establish the position of the team after the last World Cup..on that front mission accomplished.
"But I think everyone associated with the programme, from the players to Bob to those of us involved in the administration feel that it was an opportunity missed," he said, referring to the second round loss to Ghana.
Gulati also confirmed that he and Bradley had held "exploratory talks" with England manager Fabio Capello about taking on a role with the Federation, over two years ago, before the Italian decided to take up the job with England.
