The 45-year-old actress and the 25-year-old comedian – who was previously engaged to Ariana Grande – are said to have talked about going away for a romantic vacation, so they can “get to know each other better”.
A source said: “Pete and Kate have been dating since meeting at the Globes party.
“They want to keep things low key – Kate is recovering from being hospitalised, Pete just went through a really tough time very publicly – but it’s hard as they can’t keep their hands off each other in public.
“They’re planning a holiday to get away from the cameras and get to know each other better.”
The couple were first spotted together at a Golden Globes afterparty last month, and they were seen holding hands last week after his comedy show in Los Angeles, but their next PDA could be in the likes of Bali or Hawaii.
The source added to The Sun Online: “It’ll be them with a group of friends, somewhere beachy like Bali or Hawaii.
“They want to take the pressure off and see where the relationship will go.”
And Ariana – who was engaged to the ‘Saturday Night Live’ star from June last year until they called things off in October – doesn’t seem fazed by her ex’s new romance.
When asked by TMZ if she thinks Pete and Kate make a good couple, she replied: “So cute.”
What’s more, Ariana is said to be focusing on the release of her new album, ‘Thank U, Next’, which dropped on Friday (08.02.19), rather than Pete’s relationship status.
A source recently said: “Ariana isn’t bothered at all. The focus is entirely on the album coming out on Friday and can’t wait for fans to hear.”
Kate was admitted to hospital last month after suffering a ruptured ovarian cyst.
She wrote on Instagram: “Turns out a ruptured ovarian cyst really hurts and morphine makes me cry. So thankful to everyone who looked after me #wobbly (sic)”