Jenna Bush Hager said her husband, Henry, wouldn't mind being related to a royal
Credit: Nati Harnik/AP

Maybe Jenna Bush Hager doesn’t have the matchmaking chops after all!

During an appearance on Access Hollywood, 34-year-old Bush Hager said her attempt to set her twin sister Barbara Bush up with Prince Harry didn’t quite go as planned.

“My sister’s humiliated,” Bush Hager said when asked if her matchmaking attempt was successful.

Bush Hager tried to play cupid earlier this week during a Today show interview with the 31-year-old prince, telling Harry that her twin sister Barbara is “available” – “I’ll give you her number,” she joked to the royal.

Jenna admitted to Fox that her sister was irked afterwards – “she killed me” – but that the royal matchmaking opportunity was irresistible “because of course, [Barbara] should be a princess.”

But the family might want to hold off tiara-shopping. Jenna also confessed that she hasn’t “yet” actually given Harry her sister’s phone number.

And if her sister isn’t interested in the prince – she knows someone else who is, she said.

Henry Hager, my husband, and I are,” she joked on Access Hollywood. “Wouldn’t you wanna be sister-in-law and brother-in-law to a prince?”

“Come on! There’s all those palaces we could borrow!” she said, noting that she was “just kidding.”

Bush, who is known to keep her love life under wraps, was last romantically linked to Franck Raharinosy, the co-founder of SPiN – a high end social ping pong club with locations in New York, Toronto, Los Angeles, Chicago and San Francisco, according to the Daily Mail. Before that, she was linked to Miky Fabrega, a painter and creative consultant in Panama. The two dated for at least four years.

Bush hasn’t publicly commented on her sister’s friendly exchange with the prince. But Harry seemed on board with the pairing, jokingly telling Bush Hager, “We can talk maybe off air.”

Harry split from Cressida Bonas in April 2014 but the two remain close and often catch up with each other, a source previously told PEOPLE.

He also remains friendly with former girlfriend Chelsy Davy. The two dated on-and-off for about seven years before calling it quits in 2011.

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Despite his status as “one of the world’s most eligible bachelors,” Harry told PEOPLE in last week’s cover story that the prospect of having children isn’t far from his mind.

“There have been moments through life, especially when we do a tour abroad, when I think, ‘I’d love to have kids now,’ ” he said.

“There’s no rush. I think I tell you what: There’s been times I’ve been put off having children.”