Rife advised Davidson to be cautious in his interview with the outlet.
Kate - who has 20-year-old daughter Lily with former partner Michael Sheen - recently admitted she likes the idea of having another child in the future.
Rife, a 23-year-old comedian and actor, and Beckinsale, 45, dated back in 2017.
He then added, "I hope they're both happy".
"A lot of ups and downs".
They were first spotted canoodling at the Golden Globes after-party at the beginning of the year and have made several low-key appearances together since - the pair were seen leaving one of Davidson's recent comedy shows hand-in-hand before heading back to his hotel.
Paul Manafort, Former Trump Campaign Chairman, Sentenced To Just Under 4 Years
FILE - In this December 11, 2017, file photo, former Trump campaign chairman Paul Manafort arrives at federal court in Washington. Ellis imposed the sentence of 47 months in prison on Manafort , 69, during the hearing in Alexandria, Virginia .
Robert Pires names top candidate to replace Maurizio Sarri at Chelsea FC
I have to find space also for him'. "He's 24, done nothing in the game and feels he can challenge the manager like that".
Trump serves fast food to North Dakota State football championship team
On Saturday, Head Coach Matt Entz of the NDSU Bison told the Grand Forks Herald that the visit was an important morale booster. While the President's physical last month showed him to be in decent health, it also indicated he was clinically obese.
Beckinsale and Davidson, 25, seemed to confirm dating rumors on Sunday when they were pictured making out in Madison Square Garden during the hockey game between the New York Rangers and Washington Capitals.
Previous insider reports have been claiming that she really likes Pete and that she is not just a rebound for him after the split from Ariana.
The Queer Eye star even found the humour in it, tweeting the photo with the caption, "Love this pic, where'd you find it guys?"
Following the sporting event, which served as official confirmation of Kate and Pete's fledgling relationship, several memes were created, including one which questioned why the actress was with funnyman Pete, who represents "guys with problems with childhood", while "wholesome guy" Antoni was ready and available.
Porowski has previously described his sexuality as "fluid".