Lee Hae-chan was quoted by the Seoul-based Yonhap news agency as saying he had been led to belief the pontiff wishes to travel the North Korea in early 2019.
The chairman of the ruling Democratic Party told colleagues: "I heard that there is talk that Pope Francis wants to visit North Korea next spring".
Last week, the South Korean president's office said leader Moon Jae-in 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.
It is expected a formal letter of invitation from the North Korean premier will be given to Pope Francis when Mr Jae-in meets the pope at the Vatican later this week.
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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