Hilton was spotted in the company of Cavill at a party before the 72nd Golden Globes ceremony, on Friday, in Los Angeles.
The two were reportedly then photographed while leaving together in the same taxi, at an event at the Chateau Marmont Hotel.
“Henry and Paris had a great time together on Friday night, and left the Chateau Marmont together, giggling like schoolkids,” a source told the Daily Mirror.
“Everyone could see the chemistry between them. Paris was fluttering her eyelashes at him like crazy and Henry was loving the attention.”
No representative of the two stars has commented on these speculations.