PCB Chairman Shahryar Khan said that he has mentioned all the details of the series in the letter and hoped that the letter will soon be responded.
He termed Nawaz Sharif “a good cricketer” who once played alongside him against Zimbabwe.
“I hope the prime minister will make a good decision”, he said.
Pakistan has been playing their home series in the United Arab Emirates because of security fears at home, but India have refused to play there for the upcoming tournament.
India and Pakistan have not played a full series since 2007. New Delhi halted all cricket matches with Pakistan following the 2008 attacks in Mumbai, although they did play a limited-overs series in 2012.
India blamed militants based in Pakistan for the attacks which left 166 people dead.
Last month, hardline Hindu activists sabotaged talks between India and Pakistan cricket officials in Mumbai, underscoring the anger still felt by some.
Under a 2014 memorandum of understanding, both countries’ cricket boards had agreed to play six series between 2015-2023, with four to be hosted by Pakistan. But all series were subject to clearance from their respective governments.
Sri Lanka on Tuesday officially offered to host the series between the two South Asian teams.
Sri Lankan officials said that with time running out, the series would be shortened to limited-over matches if played on the island.