Pakistan Cricket Board (PCB) chief executive Wasim Khan has urged England to send a team to the country before their scheduled return in 2022 after Azhar Ali's side agreed to travel to Britain during the coronavirus pandemic.
England have not visited Pakistan since 2005/06. An attack by armed militants on Sri Lanka's team bus in Lahore in 2009 ended major cricket tours for a decade.
But Sri Lanka, Zimbabwe, West Indies and Bangladesh have all made the trip.
"England are due to tour in 2022, and we'd love to have them coming over well before then for a shorter tour," Khan told Sky Sports on Wednesday.
"It's something that we'll speak to the ECB (England and Wales Cricket Board) about," he added.
Pakistan are currently playing the first Test of a three-match series at Old Trafford, which follows an England-West Indies series last month.
Both teams, among the poorer Test nations, have been praised for travelling to Britain, which has been hit hard by the COVID-19 outbreak.
Khan told a recent PCB podcast he hoped England would do the "right thing by us as well" in going ahead with their 2022 tour.
England coach Chris Silverwood, asked if the advent of the Twenty20 Pakistan Super League, which has featured several English players, had increased the prospects of an England tour, told reporters: "I think we are getting there.
"Personally, I would have no problem with that. I've never been to Pakistan so it would be nice to go there."
The former England paceman jokingly added: "I know our batsmen would look forward to batting on their wickets."
"For me it's great that it's back at the top of the conversation."
Meanwhile Khan was pessimistic when asked about the prospects for a resumption of the great rivalry between Pakistan and India.
Political tensions mean the neighbouring countries now rarely meet outside of International Cricket Council events and they have not played a Test series against each other since 2007/08.
The chief executive told Sky: "It's a question I get asked more than any other question from fans from both sides: 'Can India and Pakistan play again?'
"It's going to be difficult, I would say, whilst the current government is in place in India.
"We've actually got a cordial relationship with the BCCI (Board of Control for Cricket in India) but they have to go to their government for permission to play against us.
"I can't see that happening any time soon."