Andy Cohen welcomed his son Benjamin Allen in February 2019 while Anderson Cooper's son Wyatt Morgan is just over 1 week old

By Benjamin VanHoose
May 06, 2020 03:57 PM

Anderson Cooper is outfitting his new addition with baby Benjamin Cohen's outgrown wardrobe.

Speaking with Stephen Colbert on The Late Show on Monday, the journalist, 52, opened up about parenting his 1-week-old son Wyatt Morgan, whom he welcomed via a surrogate on April 27. Cooper admitted that he's relying on pal Andy Cohen — who is dad to 15-month-old Benjamin Allen — for baby clothes at the moment.

"He's actually really helped me because my son is entirely wearing hand-me-downs from Andy Cohen's son," said Cooper, who then explained his reasoning: "I'm inherently cheap, I like a good value ... and, first of all, it's a pandemic — I was planning on going shopping, which I hate to do, and then, like, online shopping, how do you do that for baby clothes?"

He added: "I don't know, it just seemed weird. So, yeah, he just gave me all the clothes."

The CNN anchor also joked that watching Cohen, 51, become a dad assured him that he was ready for parenthood himself.

"He's been encouraging me all along," said Cooper. "And I figured, you know, if he can do it, well that sort of gave me the final push. Well, like, if he's got a kid, then — and his kid is amazing; Benjamin is incredible."

Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories

On Monday, Cohen revealed on his SiriusXM radio show that the Cooper household is sharing something else from Benjamin's early development: his nanny! The TV personality confirmed that his nanny left to be a caregiver for Wyatt.

"We had long planned this transition, but I certainly didn't expect it to happen during a quarantine, of course," said Cohen. "So we had to really handle this hand-off from one home to the next very carefully, but we did, and she is now with Anderson and I know she's gonna get Wyatt on a great sleep schedule just like she got Ben."

Added Cohen: "I'm so happy for Anderson. We've been talking about this for a long time and I have been really enjoying Anderson coming over. His visits with Ben have taken on a special significance since we both knew for a while that Anderson was planning on [becoming a dad] himself."

RELATED VIDEO: Andy Cohen Reveals His Son Ben's Former Nanny Is Now Anderson Cooper's Son Wyatt's Nanny

Cohen said he is also "so excited" for Ben and Wyatt "to grow up together and be friends and get to know each other."

"It's a great age difference for them to be pals, only one year," he said. "It was fun over this past year for Anderson to come over and for me to watch him with Ben and know that this would be his thing, and he was obviously paying attention to a lot."

Cohen celebrated Wyatt's arrival on Instagram last week, writing alongside alongside a photo of Cooper and his new baby boy: "'New life, new hope!' Wyatt Cooper, you couldn't have come at a better time! I know a friend who can't wait to meet you!"

As information about the coronavirus pandemic rapidly changes, PEOPLE is committed to providing the most recent data in our coverage. Some of the information in this story may have changed after publication. For the latest on COVID-19, readers are encouraged to use online resources from CDC, WHO, and local public health departments. PEOPLE has partnered with GoFundMe to raise money for the COVID-19 Relief Fund, a fundraiser to support everything from frontline responders to families in need, as well as organizations helping communities. For more information or to donate, click here.