The notoriously private Kanye is thought to be the one pushing for a lavish celebration, while Kim, who has walked down the aisle twice before, is said to prefer a more low-key affair.
"Kanye wants something really cool and big and over-the-top," an insider reportedly told Us Weekly. "They'll most likely have a destination wedding. He has never been married before and wants a big wedding."
Kim, meanwhile, has reportedly said that she wants a small scale celebration, with about 30 to 50 people on the guest list.
It is speculated that Kim and Kanye could choose Paris as their wedding destination, a city that is close to the rapper's heart. Kanye recently spent time in the City of Lights where he made his latest album Yeezus.
Unlike Kim's last wedding to basketball player Kris Humphries, which was documented in a two-hour special of Keeping Up With The Kardashians and viewed by two million people, Kim and Kanye's wedding will most likely be a private affair and at present they are denying immediate plans to marry.
Kanye is one to keep his personal life guarded, and has previously said that his daughter will not grow up in the limelight or appear on the Kardashians' hit reality TV show at such a young age.
The rapper is said to be completely in love with his girlfriend and newborn daughter, and ready to settle down. He has been busy building a nest for his new family, and was recently spotted furniture shopping in Beverly Hills.
Kim and Kanye are getting ready to move into their £7million Bel Air mansion and their latest purchase was reportedly six of the limited-edition Savoir Royal State Beds, which totalled £750,000.
The couple bought the sumptuous mansion together at the start of this year and have meanwhile been living with Kris Jenner, Kim's mother and manager, in her Calabasas mansion while their house is being refurbished.