The incident happened earlier this week, with Radar Online reporting that Jack went to their home at around 1 a.m. and ended up punching the man in the head.
Gabel reportedly decided against pressing charges, with sources claiming Jack had been "uncooperative with police".
Yahoo Entertainment confirmed that the North Hollywood Division of the LAPD took "a report involving Mr. Osbourne" and it's "an ongoing investigation". Jack "hauled off and punched" Gabel, according to TMZ's sources, before making a quick exit.
Jack and Lisa split in May, with the star's wife filing for divorce just three months after the former couple welcomed their third and youngest child, daughter Minnie Theodora, now five months. However, it doesn't appear that Jack will face any criminal charges as he is refusing to cooperate with authorities and the alleged victim doesn't want to press charges.
In May, Lisa quickly filed for divorce, but they were spotted out soon after with their children.
A request for comment and additional details from Jack's rep wasn't immediately returned. Jack's mother is Sharon Osbourne, who is now one of the five co-hosts on the day time series, The Talk, on CBS.
Jack hasn't let on that there has been drama, posting some cute pictures of his kids during a trip to a farmers' market on social media Wednesday.
The reason Jack was so upset, sources close to the situation tell TMZ, is because he thought he and Lisa were on track to fix their relationship and be a family again. "Lots of love Jack and Lisa".
Speaking about his diagnosis in October a year ago, Jack said: 'I look at my daughters and, not to get overly sappy, but there is that notion where if they get married, I might not be able to walk them down the aisle, I can get kind of heavy with it'.
In 2013, Lisa had a miscarriage in her second trimester.
It's unclear when Lisa began dating Gabel, and he hasn't addressed the drama on his social media either.
Just days after the divorce news broke, a TMZ cameraman caught Jack and Lisa out with their kids in Studio City, California.