The 22-year-old goalkeeper joined the Reds in July 2018 after spells with Chelsea, Watford and Sheffield United.
In total, she made 17 appearances across her two seasons with LFC Women.
In a farewell message, Kitching said: “My experience while at LFC Women has taught me a lot. I’d like to say thanks to the fans for their constant support and to my teammates for always being there for me. I have made some friends for life.”
LFC Women manager Vicky Jepson thanked the player for her contribution.
She said: “Myself and the backroom staff would like to thank Fran for the two years at our club. During Fran’s time we have seen her step up and make some big saves during important moments in games.
“We would like to wish her the best of luck with the rest of her football career and I’m sure our LFC fans will join me in saying our goodbyes.”
Everyone at Liverpool FC would like to thank Fran for her contribution to the team and wish her every success in the future.