The 'Mercy' rapper - who is expecting his first child with the 32-year-old reality TV star in early July - is trying to convince the fashion editor to put the brunette beauty on the US cover of Vogue magazine.
A source told Star magazine that while Anna thinks that Kanye, 35, is ''terrific'', she thinks his girlfriend of almost one year is ''the worst thing since socks and sandals''.
The insider also claimed that the style icon said Kim would appear in the esteemed fashion magazine ''over her dead body''.
Anna allegedly ignored Kim at New York Fashion Week last September and the insider claims the only way Kim has a chance of appearing in the American version of the magazine is in a feature introducing her newborn baby to the world.
Kim and Anna's feud has been well documented in the past.
The 'Keeping Up With The Kardashians' star was banned from attending the star-studded Met Gala in New York last year with Kanye because Anna believed she ''didn't fit the bill''.
A source previously explained why Kim was not invited: ''Anna hates Kim. Why would she be invited to the event? It is all the biggest stars in the world and Kim doesn't fit that bill at all. The Met Gala is $25,000 a ticket, but Kim couldn't even buy her way in.''
Kanye is set to perform at this year's prestigious ball on May 6 but it is uncertain if Kim will attend, as it is the same day her divorce trial against Kris Humphries is set to begin.