Kathie Lee Gifford's Daughter Cassidy: My Family Was Almost the Kardashians!

America got to know Cassidy Gifford because her mom Kathie Lee Gifford regaled Live! With Regis and Kathie Lee fans with anecdotes until she left the show in 2000, but it turns out we could have been keeping up with the Giffords this whole time!

“When I was younger, people kept making offers for different reality shows and stuff,” Cassidy – who makes her debut in a leading role in summer horror film The Gallows (out Friday) – says in the new issue of PEOPLE.

In fact, E! producers initially approached Kathie Lee, now 61, for a family-style reality series, but the Today personality actually recommended they pitch the show to her longtime pal Kris Jenner, thus making her responsible for a little show called Keeping Up With the Kardashians.

Had Kathie Lee said yes, what would a Gifford family TV show look like?

“One of the [propositions] was just the most absurd thing in the entire world: They wanted some family to come live with us and pretend they were long-lost relatives that didn’t have anywhere to go,” recalls Cassidy, 21.

“Everyone wouldn’t know but my mom, and they would bring random farm animals like sheep and cows to our house. So my mom would be, like, swearing that they’re our family members – they’d move in with us, they’d speak a different language and then just see what happens.”

RELATED VIDEO: Kathie Lee Gifford Was Originally Approached by E! For Reality Show but Recommended Kris Jenner

Despite the reality show offers, Cassidy insists her family – mom Kathie Lee; dad Frank, a former New York Giants player, and older brother Cody – is completely ordinary in spite of her parents’ fame.

“We’re like the most normal family on the planet, honestly. I’m very grateful,” says The Gallows actress. “They’re awesome. We fight a lot – don’t worry! We’re not perfect. But I wouldn’t trade them for anything in the world.”

As for the ubiquitous Kardashian-Jenner clan, Cassidy still thinks of them as the family she knew before the cameras started rolling.

“They’re some of the kindest, most generous people in the world,” says The Gallows star, who shares a particularly tight bond with the Jenner ladies. (Kathie Lee is actually godmother to Kylie and Kendall, who calls Cassidy ”godsissy.”)

“Kris was like a second mom to me growing up, and she would jump through burning hoops if I needed something,” says the actress, who moved to Los Angeles in 2012 to study English at USC and pursue acting. “My mom always said that when I moved out to L.A., Kris would be the first person to be there if I needed something.”

For more on Cassidy Gifford, pick up the new issue of PEOPLE, on newsstands Friday