The couple met with the pastor who officiated at their wedding to discuss their split, Radar Online reported.
The two-hour meeting with Pastor Joel Johnson, who has known Humphries since he was a child, took place at the basketballer's lavish lakefront home in suburban Chanhassen.
Kardashian then left the property with Johnson, while Humphries later emerged without saying a word to waiting paparazzi.
TMZ photographers had seen the 31-year-old reality TV star arrive at Minneapolis-St. Paul International Airport with a bodyguard about 5:30am local time Sunday.
She had taken a Saturday night flight from Los Angeles to see Humphries -- the first time they had met face-to-face since the shock divorce announcement.
He has rarely been seen since the story broke last week, instead spending time with family, friends and focusing on training.
"He's sad," a source told E! Online. "He doesn't want a war. He's laying low."
Kardashian announced last week that she was divorcing the NBA star after just 72 days of marriage on the grounds of "irreconcilable differences."
A report earlier Sunday said she planned to buy the 20.5 carat engagement ring given to her by Humphries. A clause in her pre-nuptial agreement allows her to buy the ring -- for which Humphries reportedly paid $2 million -- from him for the original purchase price in the event of a divorce.
A day after filing for divorce, Kardashian wrote on her official website that she "married for love" and blasted speculation that her nuptials were for the benefit of her TV shows.
She married Humphries on Aug. 20 in a ceremony that was broadcast on cable network E! as the two-part special "Kim's Fairytale Wedding."