The pair have been the subject of romance rumours following the 22-year-old actress's split from Nicholas Hoult last week after two years of being together, reported Daily Mail.
Cooper, 38, is also single after splitting from actress Zoe Saldana earlier this month.
Asked about a romance between the two at the recently concluded the Golden Globes ceremony, Cooper said, "If it didn't happen by now, it's not gonna happen. I could literally be her father."
Still, the pair certainly looked flirty inside the star-studded ballroom at The Beverly Hilton Hotel as they sat side by side.
Lawrence won the best actress trophy in the musical or comedy category for 'Silver Linings Playbook'.
