The Pontiff has been given a formal invitation, which was relayed by South Korea's leader.
The South Korean leader, President Moon Jae-in, who is Catholic, also asked Pope Francis to wish the Korean peninsula peace, reconciliation and shared prosperity.
Last week, the president's office said he was told by Kim Jong Un that the Catholic leader would be "enthusiastically" welcomed in Pyongyang.
Following a similar invitation for the then-Pope John Paul II to visit North Korea, the Vatican said a papal trip would only be possible if Catholic priests were accepted there.
North Korea has consistently been named in Open Doors' annual World Watch List as the country where persecution against Christians is worst.
The news comes four months after a much-anticipated visit between Kim Jong Un and US President Donald Trump in Singapore.
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