The American Idol host - who is also a producer on reality show Keeping up with the Kardashians - admitted on his KIIS FM breakfast show that he expects an announcement from the pair soon.
According to Metro, while discussing rumours that Kardashian had demanded a "birthday" engagement ring, Seacrest described West as being "desperate to propose to Kim".
"I think we could definitely see an update on this story on Monday," he told his co-host.
Kardashian and West have been dating for six months and are currently on holiday together in Rome. West organised the surprise trip to help celebrate Kardashian's 32nd birthday, which takes place tomorrow (October 21).
A source close to the couple also told Radar Online that West has been looking at engagement rings for some time.
"It's only a matter of time before Kanye pops the question," the insider revealed. "They are madly in love with one another and as far as Kanye is concerned he wants to spend the rest of his life with Kim.
"It's just a case of making sure the ring is perfect because she's his princess," they added.
If West does decide to propose, the pair will have to wait until Kardashian's divorce from husband Kris Humphries is officially finalised.
The socialite and businesswoman separated from the basketball star after just 72 days of marriage back in 2011, but legalities have not yet been settled.