The power couple have been attending counselling in a bid to preserve their relationship.
But the rapper is said to be speaking to lawyers this week with a view to both of them moving on with their lives.
The insider says that the stars have now stopped attending their marriage counselling sessions.
Referring to 43-year-old Kanye, they said: “He is talking to divorce lawyers this week.
The couple themselves have not yet confirmed that they are ending their seven-year marriage.
Neither responded to a request for comment from PEOPLE but the news comes less than a fortnight after other sources told the news outlet that Kim, 40, planned to file for divorce.
She is said to be working with the well-known divorce attorney Laura Wasser.
“They are just not on the same page when it comes to their future as a family,” one insider told the outlet. “And Kim is okay with it.”
The news comes six months after Kanye unleashed a blistering social media attack on the Kardashian-Jenner clan, comparing mother-in-law Kris Jenner to North Korean dictator Kim Jong-un.
During a blistering attack in a string of now-deleted tweets, Kanye claims the Kardashian-Jenner family attempted to have him admitted to a psychiatric unit.
“They tried to fly in with 2 doctors to 51/50 me,” he tweeted at the time.
He added: “I been trying to get divorced since Kim met with Meek at the Waldorf for ‘prison reform’.
“I got 200 more to go. This my lady tweet of the night … Kris Jong-Un. Lil Baby my favourite rapper but won’t do a song wit me [sic].”
Kim and Kanye who put on a united front over the Christmas break for their children – Saint, five, Chicago, two, and Psalm, one.