The former couple - who split in 2011 after just 72 days of marriage - have been locked in a bitter battle as Kris wants to annul the union and Kim wants a divorce but Kris, 28, has hinted he will grant Kim her wish if she says sorry for how she treated him.
A source told RadarOnline: ''Kris has never said he won't settle, but he has certain conditions and terms that he wants Kim to agree to that don't include money.
''Put simply, if Kim were to formally say sorry to Kris in court - and if he felt it were sincere - he would likely agree to end the marriage and avoid the trial.
''However, if Kim comes into court with an attitude and acting full of herself, Kris will absolutely take this to trial.
''The ball is in Kim's court and that pun is intended!''
If both sides are unable to reach an agreement the trial will proceed on May 6.
It was recently claimed Kim, 32, - who is pregnant with her first child with her 35-year-old boyfriend Kanye West - is ''furious'' with Kris for dragging out their divorce since November 2011 and is worn out by their ongoing battle.
A source close to the star, who has had a number of health scares during her pregnancy, said: ''Kim is furious with Kris! She wants to be divorced now and she is sick of his games.
''Kim is six-months pregnant and this would take a toll on anyone, she is no different.''