The recently-appointed Swans chief, who was dismissed by the United States following the 2011 Gold Cup final defeat to Mexico, suggested last week that the German had been eyeing the position long before he was given the nod.
Bradley felt that Klinsmann had undermined his position while commentating on the previous year's World Cup, but the former Tottenham Hotspur and Bayern Munich star has strongly denied the accusations.
"It's simply not true," he is quoted as saying by ESPN. "I could've taken the job in 2006. I could've taken it in 2010. I was not jockeying anything.
"I wish Bob the very, very best. It's a big, big moment having an American coach coaching a Premier League club. I think it's huge. He's an awesome guy. He's a good person and I just keep my fingers crossed for him."
Bradley's first match in charge of Swansea comes on Saturday afternoon when the Welsh outfit visit Arsenal.