The 52-year-old actor told People that he bonded with Bullock's 3-year-old son, Louis, over hoops.
"Louis and I played basketball together," Clooney, 52, said Tuesday at the New York premiere of his and Bullock's new space drama, "Gravity."
"There was [director] Alfonso [Cuarón] and Rande Gerber (Cindy Crawford's husband), and Louis would gravitate towards me and the guys and hang with us," Clooney said about their time on the film set.
The Oscar-winning actor then jokingly added, "It was fun, but I wish Sandy would stop telling the story, because it's totally ruining my reputation!"
Last month, Bullock, 49, told reporters that Louis preferred spending time with Clooney than with her.
"If there was a choice between me and George … my son will leave to go with George and the guys," Bullock said at a press conference at the Toronto Film Festival.
"He's a boys' boy. He has to go and talk to the men," she added. "He asked, 'Where's George and Rande?' I'm like, 'What? I don't know.' He goes, 'I need them.'"
The "Blind Side" actress said if anyone is going to monopolize her son's time, it might as well be Clooney, someone she's known for more than two decades.
"George is a good man, and I'm really proud to have known him for this time and the human being he's become," she said in Toronto.
Clooney was equally complimentary of Bullock on Tuesday.
"Sandy is the best. We've been really close friends for a long, long time," he said. "She likes to say 20 years, but it's been a little longer than that. So just the idea that I got to work with her was a blast."
Clooney said that the two became friends when she was "dating one of my best friends, a dear friend of mine for a long time."
"I got to know her long before any of us had succeeded," he said. "When she hit it big in the Sylvester Stallone movie ["Demolition Man"] - that was her big break in the film world, and we were all very excited for her."