When asked about the date, Pope Francis replied with a laugh, "I can tell you now if you like," according to the National Catholic Register.
The Vatican has yet to confirm it, and the papal spokesman says the official announcement will be made after the Sept. 30 consistory.
The source said Pope Francis was surrounded by top officials at the time of the informal reveal, including Archbishop Georg Ganswein, who will help in organizing the canonization ceremony.
Pope John XXIII is also expected to be canonized on the same day, as confirmed by Pope Francis during a papal press conference in July. He said both former pontiffs will be canonized "together."
National Catholic Register reports two other possibilities for the ceremony are Christ the King Sunday on Nov. 24 and April 27, which is Divine Mercy Sunday, according to the Catholic Church.