Osbourne apparently bought flowers for the daughter of the late Joan Rivers on her first day as a host of Fashion Police. Melissa also still serves as a producer of the series.
"@MelRivers congratulations on an awesome show tonight!" Osbourne, 30, tweeted.
"@KellyOsbourne I love you!!! The flowers are amazing and you owned the lavender carpet! Xxx #friends #mysister," Melissa, 47, replied.
The one-year anniversary of Joan's death is quickly approaching on September 4.
Osbourne quit Fashion Police after her former co-star Giuliana Rancic made an offensive joke about Zendaya Coleman's dreadlocks at this year's Oscars. Osbourne insisted Rancic's remark was racist and the pair has never reconciled or dropped the feud since.
Not long later after Osbourne left the show, Kathy Griffin quit the series claiming her humor didn't match up with the show's creative direction. The E! show executives -- including Melissa -- then decided in March they should stop airing Fashion Police for a while to allow for a breather and some genuine time to revamp the show.
Melissa had acknowledged Fashion Police was missing the mark because they no longer had Joan's stage presence and amazing comedic delivery. Joan was able to poke fun at people while still coming across caring, charming and light-hearted.
Fashion Police is currently co-hosted by Rancic and Brad Goreski with celebrity guests appearing on the show along the way. This week, Big Brother's Frankie Grande and The Real Housewives of AtlantaNeNe Leakes appeared on the show.