It was reported the pontiff had a small, curable brain tumour by the Italian daily Quotidiano Nazionale but the Vatican quickly condemned the story as "unfounded and seriously irresponsible".
The story was published just days before the end of the Catholic Church's Family Synod which has been discussing, among other things, the treatment of gay and divorced people.
Some claim Pope Francis has a more liberal stance on the issues after he famously questioned the idea of judging people.
The claims have angered many other Church leaders who feel there should be no change on the issues.
Now it has been claimed the brain tumour story was made up by conservative members to discredit the pontiff's views.
Some people attending the Synod have briefed reporters saying the story was created by the pope's "enemies" to give backing to the theory his judgement is impaired.
Cardinal Walter Kasper, a liberal from Germany, is quoted in the Telegraph as saying: "It's evident to me that some people don't like this Pope. Maybe they were trying to influence us.
"Certain people, both inside and outside the Church, are nervous about the outcome of the Synod."
He added that he thought the story was an attempt to "upset" the synod.
Papal biographer Paul Vallely told Premier's News Hour: "The Vatican is a buzz, like the best kind of Dan Brown novel, with speculation, intrigue and Machiavellian plotting.
"People are saying that this story has been put out deliberately by opponents of the Pope to suggest that his judgement has been impaired by this brain tumour."
He added it was a sign people were "deploying dubious tactics to get their own way".
"This pope wants debate, he said at the last synod everyone must speak boldly and listen with humility and I think a lot of these cardinals have remembered the speak boldly bit and forgot the listen with humility bit," he added.
Paul Vallely speaking to Premier's Hannah Tooley:
