On Friday night, the duo was spotted hand in hand leaving Pete's comedy show at the Coronet Theater in West Hollywood. Kate, by the way, attended both of Pete's standup shows on Friday night.
Neither Pete nor Kate said anything as photographers shouted questions to them during their short walk to an awaiting car.
TMZ reported that the two headed to a hotel in Santa Monica.
Last month, multiple media outlets said that Kate, 45, and Pete, 25, seemed to have a real connection at Netflix's Golden Globes after party.
E! claimed the two sat closely together on a couch on a smoking patio for about an hour, looking "very cozy."
"She was very flirty with him and there were definitely some vibes going on," a source told E!. "Pete was smiling and laughing with her and she was all about him."
People magazine also reported on January 7 that the two "talked intently for most of the night."
Pete has been single since he and Ariana Grande split and called off their engagement in October 2018. Kate was last linked to 23-year-old comedian/actor Matt Rife. She and producer Len Wiseman ended their marriage in 2016.