"He's willing to hand it over to Kim and Kanye for their new baby girl if they want it, because selling it 'just kind of seems wrong, '" the site reported. The baby girl is couple's third child after daughter North and son Saint.
Kim is keen to make sure people are pronouncing the name correctly.
One fan compared the name to a pizza, joking: "I'll have the Chicago West please".
She wrote that the baby was born Monday at 12:47 am at seven pounds, six ounces.
Meanwhile, a lawsuit filed by Blac Chyna against Kim Kardashian West and mother Kris Jenner has been "tentatively" dropped, .
Kerber beats Sharapova in 3rd round in Australia
Kerber raced through six straight games, taking the first set in 29 minutes and breaking at the start of the second. In complete contrast in the final match, Agnieszka Radwanska is also a decent favourite to defeat Su-Wei Hsieh.
Kardashian West then retweeted a post which said Chi was pronounced as "Shy".
The report states that Kim - who is a prolific Instagram user with 106million followers - immediately rejected money from outlets for the first pictures.
But instead they chose Chicago - the name of Kanye's home city!
The power couple who welcomed their third child via a gestational surrogate this week, revealed today through Kim's pay-per-view app.
In a 2015 interview with Q Magazine, he said: 'If I had never moved to L.A. she'd be alive.