Clooney, 47, put on a look of mock bemusement.
"I am so surprised to hear that question. That is honestly the first time I have been asked that," Clooney said. "I am getting married and having a child today."
Pitt, whose brood has grown to six children with the birth of twins Knox Leon and Vivienne Marcheline last month, offered to share his children with Clooney, adding deadpan: "I'll have two more by next year."
The movie, which premieres Wednesday at the Venice Film Festival, is a tale about idiots - and what happens when their worlds collide.
Pitt, 44, looked flustered as a Spanish TV journalist pushed her way to the front of the press conference dressed in red gym shorts similar to garb he wears as a gym trainer in the film. She asked Pitt if he would help her work out.
"It's a movie," Pitt reminded her.
"Would you run after me?" she asked Clooney and Pitt.
"I think we're more likely to be running away from you," Clooney replied to laughter.
Several times Clooney good-naturedly ran interference for Pitt, who was peppered with questions about his personal life. Asked about the infants, Clooney intervened: "The twins are fine," then joked that he and Pitt were sitting at opposite ends of the podium because of a restraining order.
And when another questioner asked if they would rather win an Oscar or fall in love with an Italian woman in Venice, Clooney warned: "Don't answer that, Brad."