Francis, 88, was admitted to the hospital on February 14 with a severe respiratory infection that has required evolving treatment.
The pope has only been seen by the public once during his hospital stay, in a photo the Vatican released last week, showing the pontiff at prayer in a hospital chapel.
Francis wants to come to the hospital window around noon on Sunday to give a greeting and blessing, the Vatican said in a brief statement on Saturday.
The pope usually offers a weekly noon-time prayer in St. Peter's Square on Sundays. Francis has not been able to do this since February 9, before going to hospital.
The Vatican said Francis was not expected to deliver the prayer this Sunday, in a sign that the pope is still recovering from pneumonia, but would come to the window for a greeting.
Francis is prone to lung infections because he had pleurisy as a young adult and had part of one lung removed.
His hospitalization has been the most serious health crisis of his 12-year papacy, and the longest he has been out of public view since his election as pontiff in 2013.
The latest Vatican bulletins about the pope's medical condition have been cautiously upbeat. On Friday, the Vatican said Francis had been reducing his use of high-flow oxygen to help breathe.
One senior cardinal, however, said on Friday that it could take time for the pope to "relearn to speak" after using oxygen during his hospital stay.
"The pope is doing very well, but high-flow oxygen dries everything out," said Cardinal Victor Fernandez, the Vatican's chief doctrine official. "He needs to relearn how to speak, but his overall physical condition is as it was before."
The Vatican has not given a timeframe for the pope's discharge from hospital, but plans for a meeting with Britain's King Charles on April 8 have raised the possibility that Francis could be back at his Vatican residence by then.
