Doctors late Thursday reported a "marked improvement" in the condition of the pontiff, who was admitted to Rome's Gemelli hospital on Wednesday, and said he could be home "in the coming days."
Cardinal Giovanni Battista Re, dean of the College of Cardinals, told the Adnkronos news agency Friday that "based on the information I have, the pope will leave Gemelli tomorrow."
Medical staff said in a statement late Thursday that Francis was suffering from an "infectious bronchitis which required the administration of antibiotics".
The pontiff could be back home in the Vatican "in the coming days", it said.
He expressed hope that Francis would be able to preside over services for Holy Week and Easter, Christianity's most important holiday, which begin with this weekend's Palm Sunday celebrations.
The Vatican did not respond to requests for confirmation.
The pope's admission to hospital, just weeks after he marked 10 years as head of the worldwide Catholic Church, has sparked widespread concern while also fueling speculation about his future.
The Argentine, who had part of one lung removed as a young man, has suffered increasing health issues in recent years, has repeatedly said he would consider stepping down if his health failed him, following the example of his predecessor Benedict XVI - but said in February that for now, he had no plans to quit.
The pontiff said Thursday that he was "touched by the many messages" he was receiving in hospital, thanking on Twitter those praying for his recovery.
Among them is US President Joe Biden, only the second Catholic president in US history.
"Jill and I are keeping Pope Francis in our prayers and send our best wishes for his swift and full recovery," Biden tweeted.
His predecessor Benedict XVI, who died on December 31 aged 95. shocked the world in 2013 by becoming the first pope since the Middle Ages to resign, citing his declining physical and mental health.
Francis has said he would follow suit if he was unable to do his job.
But he has cautioned that papal resignations should not be the norm, and said in an interview in February that the idea was currently not "on my agenda."
