The date was decided during a closed-door meeting of cardinals at the Vatican, the source said, according to Reuters.
Some 135 cardinals from across the world, including four Poles, are eligible to take part in the conclave and decide who should be the next head of the 1.4-billion-strong Church.
Polish cardinal Konrad Krajewski, a close ally and charity envoy of Pope Francis, is among those being considered as a possible successor, according to media reports.
Pope Francis, who was elected in 2013, died on Easter Monday at the age of 88.
His funeral on Saturday and a procession through Rome to his burial place at the Basilica of St. Mary Major attracted crowds
estimated at more than 400,000, according to Reuters.
Polish President Andrzej Duda and lower-house Speaker Szymon Hołownia were among those who attended the ceremonies.
The conclave, a secretive gathering of cardinals to elect the next pope, will convene in the Sistine Chapel after a period of mourning.
(gs)
Source: IAR, PAP, Reuters