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After a report claimed Pamela Anderson and Liam Neeson's romance was faked to promote The Naked Gun , sources tells PEOPLE "everything between them has been genuine"

"Neither would ever take part in a publicity stunt," says the source

In July, an insider said the costars had a "budding romance in the early stages"

Pamela Anderson and Liam Neeson 's romance is not a publicity stunt, sources tell PEOPLE after reports surfaced claiming otherwise.

"Everything between them has been genuine. Neither would ever take part in a publicity stunt. They have a great time. Neither of them needs the publicity," a source close to the film tells PEOPLE.

Another insider says, "Their relationship isn’t just for show. They have a real connection. There’s no incentive for either of them

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