The 29-year-old presented the X Factor's spin-off Xtra Factor with the television host in 2013 while he was also a panellist on ITV2 show Viral Tap, which was presented by Flack in 2014.
“Obviously we worked together lots, but she was a really good mate of mine," he told The Sun.
“Like she was one of my best friends in the world. And it’s weird, actually when I got the call to go onto the show this week, she would have been one of the first people that I'd have rung.”
“So I had a real pang of sadness that this wasn't something I could talk to Caroline about and would have had, you know, a really good laugh about. Like what I'd look like in the costumes and all that kind of fun, silly stuff. And she would have been amazingly supportive."
Richardson added that Flack had "helped [him] in everything" when she was alive.
The Love Island presenter sadly took her own life last February at the age of 40. She had won a dance competition herself having been crowned Strictly Come Dancing champion in 2014.
With the departure of Rufus Hound and Robin Johnstone, comedian @MattRichardson3 and his pro-skater partner @vickyogden1 will be joining the line up from this weekend ⛸ #DancingOnIce pic.twitter.com/xUxzFMSKvh
— Dancing on Ice (@dancingonice) February 3, 2021
Richardson will be skating with professional Vicky Ogden as he takes over Hound's slot after the comedian tested positive for the coronavirus after the show updated its COVID-19 protocols.
Read more: Dancing on Ice has no reserve skaters left
He isn't the only late entrant to the competition as Olympic gymnast Amy Tinkler stepped in last week to take Denise van Outen's place when she had to drop out due to a shoulder injury.
Despite not being part of the original cast, Tinkler managed to avoid being in the skate off which saw Olympic skier Graham Bell sent home.
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Watch: Laura Whitmore pays tribute to Caroline Flack