PCB chief executive Wasim Khan confirmed the development.
"We'll try to look for a possible window for this tour - and if not 2021, we’ll definitely try to plan a series in 2022 season," Pakistan Cricket Board (PCB) chief executive Wasim Khan told AFP.
"A cricket series between Pakistan and Afghanistan could be a harbinger of love and peace between the two countries," he added.
Although Afghan national side toured Pakistan in May 2011, they only played a second-string side and matches were not given first-class status.
As a member of world cricket's second tier, Afghanistan's generally play against teams such as Ireland, Scotland and Hong Kong.
However, Afghanistan’s victory over Pakistan in a warm-up match ahead of the World Cup in England led to a massive celebration in Kabul.
The two countries have faced each other in one ODI and one T20I so far, with Pakistan winning both the contests in UAE.
"A strong Afghanistan means a strong Asian block... so Pakistan will continue to play its part and help Afghan cricket," Wasim stated.
Afghanistan are also slated to host Pakistan for three ODIs as part of World Cup 2023 Super League, most likely to be played in the United Arab Emirates.
(With AFP inputs)