Pakistan want Sri Lanka to visit in the second half of April after Bangladesh agreed to play earlier in the month. Australia were due to tour from March 29 to April 29.
"Sri Lankan Board's president Arjuna Ranatunga is coming to Pakistan on Thursday and I hope that he will agree to send his team for a one-day series," Pakistan Cricket Board chairman Nasim Ashraf told AFP.
Bangladesh will play five one-day matches next month here, Ashraf added. Sri Lanka are touring the West Indies until April 15.
Ashraf also brushed off doubts over Pakistan's hosting of the ICC Champions Trophy in September and the Asia Cup in June and July.
The International Cricket Council (ICC) on Tuesday confirmed Pakistan will host the elite Champions Trophy from September 11-28. But it named Sri Lanka as an alternative venue in case Pakistan is not cleared on security issues.
"ICC is sending an advanced party to Pakistan on Thursday which will assess facilities and security in Pakistan and we hope to host the event in a befitting manner," Ashraf said.
Separately, an Asian Cricket Council delegation is in Pakistan and will announce the dates and venues for the Asian Cup in Lahore on Thursday.
"We have unequivocal confirmation from Sri Lanka, India, Bangladesh, United Arab Emirates and Hong Kong to come for the Asia Cup," said Ashraf.
Ashraf also said he held meetings with Cricket Australia (CA) chief Creagh O'Conner in Dubai and hoped that the postponed Australia series will be rescheduled very soon.
CA has invited the PCB chairman to visit Australia to fix new dates for the tour. Australia's tour had been in doubt for months amid questions about security following a series of major blasts and serious political upheaval.