Bradley, who led the United States into the second round of the World Cup finals in South Africa where they lost to Ghana, has been linked with English Premier League club Fulham.
GEAR: Get a USA shirt
"I think he would do well, 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," the Old Trafford supremo told reporters.
Bradley's contract with the U.S. runs out in December and the shaven-headed former MLS coach has not been offered a new deal with a number of foreign coaches linked to the role.
"I think he did a fantastic job and I am surprised the USA have not sprinted to his house and given him a new contract, I must say that," said Ferguson ahead of Wednesday's game between United and the MLS All Stars.
Bradley has visited Manchester United's training ground to study Ferguson's work at close hand and the Scotsman said a switch to a European club might be just what Bradley needed.
"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 for that matter," Ferguson said.
"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."
The red Devils lost 2-1 to Kansas City Wizards on Sunday and could be without John O'Shea and Darren Fletcher who have niggling injuries for the game against the MLS team which is expected to draw a capacity 71,000 crowd to Reliant Stadium.
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