The pair were featured on Friday's episode (22 November) alongside Kylie Minogue, when Banks – who is promoting her new Charlie's Angels film – said: "The first time I ever met you was at the Golden Globes."
Uncertain, Gervais replied: "Yeah, you came over to..." before Banks cut him off by saying: "You do not remember that – there's no way you remember that."
Banks laughed as the comedian then admitted that his researcher reminded him of the moment backstage.
"You're very sweet," she said, as Gervais attempted to explain why he couldn't remember in the first place.
"There were loads of people coming over, it was crazy," he said, as Banks interjected: "Really? You were standing by yourself when I came over."
Gervais – who will return in the second season of his Netflix show After Life next year – will host the Golden Globes for the "fifth and final time" in 2020.
It opened to a dismal $8 million (£6.1m) in its first three days of release, with the film costing a reported $48m (£37m) to produce.
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