American lead his country to a Round of 16 appearance in South Africa
Bradley has been tipped with a move to Fulham to replace Roy Hodgson, who moved to Liverpool this summer.
The American’s reputation has been helped by his job leading the USA to the Round of 16 in the World Cup this past summer, leading his team to the top spot in Group C over Fabio Capello’s England side.
United boss Ferguson is adding his name to the list of supporters of Bradley moving to Europe, acknowledging that the American would do well in the Premier League.
"I think he would do well," Ferguson told Sky Sports.
"I like Bob, I like his approach, I think he has a steely determination about him and he goes into a lot of detail in his coaching."
Ferguson was surprised that the United States national team have not offered Bradley a new deal with his current contract set to expire in December.
"I think he did a fantastic job (at the World Cup) and I am surprised the USA have not sprinted to his house and given him a new contract, I must say that.”
Whether European clubs are interested in Bradley has not been determined yet, but Ferguson thinks that the 52-year-old might want to test himself.
"He may want the challenge himself, I think that what he has achieved with the USA has been very good.
"He is a young man and I don't think there is anything wrong with taking a challenge in Europe or England.
"I know he has been linked with Fulham and I don't think it is beyond his boundaries at all. I think he is very capable of taking on a challenge like that."