"She may consider doing it again but the offer would have to be really high," the insider added. "It's a lot of extra work for her."
As for Leakes, who's starred on The Real Housewives of Atlanta since 2008 and appeared on Fashion Police as a guest in 2013, was also initially rumored to replace Rivers following her September 4 death. The spot eventually went to Kathy Griffin.
Leakes had also competed on the fourth season of The Celebrity Apprentice and Dancing with the Stars' eighteenth edition.
Osbourne's Fashion Police departure comes on the heels of a controversy in which her co-host Giuliana Rancic had made an offensive comment about the dreadlocks Zendaya Coleman rocked at this year's Oscars. Rancic said Coleman's hair must have smelled like "patchouli oil and weed," which sent Coleman on a social media rant and prompted Osbourne to publicly express her disapproval.
Osbourne is apparently friends with Coleman, so her sudden exit from Fashion Police doesn't appear to be a coincidence. Rancic, however, apologized to Coleman for her comments on two separate occasions -- on Twitter and during a segment on E! News.