Australia have not toured Pakistan since 1998 but Khan hopes they can be persuaded to play there.
"I will ask the question," Birmingham-born Khan told ESPNcricinfo.
"We will continue to offer them the highest level security and, if they have any concerns, we will act to meet them."
Sri Lanka returned to Pakistan in 2017 for a one-off Twenty20, while West Indies played a three-match Twenty20 series in Karachi in April this year.
Khan said he wanted to speak with other boards to see how he could help get regular international cricket back to Pakistan.
"It will probably be a process of baby steps," Khan said.
"I need to sit down with other boards and ask them: where are the gaps in our plans that worry you? What can we do to assure you? What will it take to get you to come back? I want to hear what concerns they have and find a way of meeting them."
English county teams would be invited to use the PCB academy in Lahore for pre-season training, said Khan, who remains Leicestershire chief executive until the end of January.
"We have excellent facilities. We have a great passion for the game. If we can get more foreign players coming to Pakistan more often, hopefully we can normalise playing in the country again."
(Reporting by Amlan Chakraborty in New Delhi; editing by Peter Rutherford)
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