Kim Kardashian West is determined to ''make it work'' with Kanye West following his shocking divorce claims.

The 43-year-old rapper claimed last week in an explosive Twitter rant he has been trying to divorce his wife Kim for two years, which led the 'Keeping Up with the Kardashians' star to issue a statement about Kanye's mental health, before flying to Wyoming to talk things through with him.

Kim has since flown back to Los Angeles without Kanye to be with their children - North, seven, Saint, four, Chicago, two, and Psalm, 14 months - but remains positive she and the 'Bound 2' hitmaker will be able to work through their differences.

A source told Us Weekly magazine: ''In no uncertain terms, Kanye told Kim he is planning on staying in Wyoming. Who knows for how long. Kim believes any path forward is tenuous at best. They are just on completely different trajectories with Kanye even refusing to acknowledge that he needs to seek help. Kim is tired and extremely sad about the entire situation.''

Whilst a second source added: ''There is a desire to make it work. She wouldn't have flown to Wyoming if she wasn't invested.''

Although she wants to patch up her romance with Kanye, Kim is believed to be ''devastated'' by her husband's Twitter rants, which also saw him claim she has been ''trying to lock him up'', as well as compare her mother Kris Jenner to North Korean leader Kim Jong-un.

Prior to his online outbursts, Kanye had broken down in tears at a presidential campaign rally, where he explained he had ''almost killed'' his daughter North, because the pair had considered getting an abortion.

A source shared recently of Kim: ''She is broken and absolutely devastated. She's in a bad place, barely sleeping, hardly eating and shutting off her closest friends. She's living in constant fear over what he's going to say or do next.''

Kanye has since issued a public apology to his 39-year-old spouse.

He tweeted: ''I would like to apologize to my wife Kim for going public with something that was a private matter. I did not cover her like she has covered me.

''To Kim I want to say I know I hurt you. Please forgive me. Thank you for always being there for me. (sic)''