The 54-year-old actress revealed as much in an interview with People on Saturday. Griffin has the opportunity to replace the late comedian as host on the E! series, but told the magazine she hasn't decided if she will accept the offer.
"Ironically, she and I talked about it many times," she said of Rivers. "It's definitely something that I've put a lot of thought into. Obviously there is an emotional tie for me because Joan was such a good friend of mine, a close friend, truly a mentor."
"We talked about everything," she recalled. "And we joked about everything on the table. So it's something that I've been thinking about for a while and I think it's something [the network has] been thinking about, too."
Rivers co-hosted "Fashion Police" with Kelly Osbourne, Giuliana Rancic and George Kotsiopoulos from its premiere in 2010 until her death at age 81 on Sept. 4. E! announced the series will continue without Rivers two weeks later, and new episodes are scheduled for 2015.
Griffin came to fame as Vicki Groener on NBC sitcom "Suddenly Susan," and subsequently starred on her own Bravo reality series, "Kathy Griffin: My Life on the D-List."
The actress also hosted "The Comedy Central Roast of Joan Rivers" in 2009.
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