A spoof Facebook group called "Liz Kendall for Conservative Leader" now has more than 3,000 'likes', while the Labour leadership candidate's official Facebook group has slightly more than 4,000.
The Tory account gives a detailed analysis of Kendall's interests.
Under 'page info', the description reads: "Liz Kendall is the most impressive potential Conservative candidate for prime minister in the last 30 years.
"This is a page for all of her supporters, and all of those people who also see her future in the Tory party.
"Please feel free to post all of your views, photographs and comments. #Kendall4Conservative."
Kendall's political views are listed as "very Conservative", with interests including Adam Smith Institute, Margaret Thatcher, Ayn Rand and Right-wing politics.
Personal interests include Neoliberalism, wealth creation, free-market, capitalism and Darwinism.
It is not yet clear who created the spoof account, but here are a couple of theories that have been posted on the page:
The #Kendall4Conservative campaign has also taken to Twitter.
Thanks to our recent followers for joining the campaign, please encourage others to do the same, together we can win! #Kendall4Conservative— Liz for Tory Leader (@LizForToryLeadr) July 6, 2015
Kendall hit headlines on Tuesday after her supporters accused Yvette Cooper's allies of politicising the fact Kendall does not have children.
In a blog for The Huffington Post on Monday, Shadow Media Minister Helen Goodman said the fact Cooper was a "working mum" had convinced her to back the shadow home secretary's leadership campaign.
Members of Kendall's campaign team interpreted it as an implicit criticism of their candidate.
We're not sure yet how well this Facebook group will go down with Kendall's camp.
Cooper and Kendall are battling Andy Burnham and Jeremy Corbyn to succeed Ed Miliband as Labour leader. The winner will be announced in September.