The two-match Test series was indefinitely postponed in March due to COVID-19 pandemic.
England spent around 10 days in Sri Lanka and played a warm-up game before the tour was called off in wake of the deadly outbreak.
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The two-match Test series is an important part of the inaugural World Test Championship.
"We are in the process of rescheduling the tours that have been postponed. England has been already rescheduled for the month of January next year but the dates have not been finalised," De Silva told Daily News.
"At the same time, we are also looking at exploring the possibility of rescheduling postponed tours and looking at the windows which are available and alternatives too."
"South Africa is one of the tours which we are looking at rescheduling. We are engaged in discussions with the member countries and see how it can be planned out."
Sri Lanka was also set to host South Africa, India in marquee limited-overs series later in the summer. But the visit by the Proteas has been officially postponed, with the India series also most likely to be suspended as well.
"There are also two other tours (apart from South Africa one) which are scheduled to take place, with India and Bangladesh due to tour Sri Lanka in June-July and July-August, respectively."
"We will explore the possibility of playing those two tours in another week or two," De Silva added.
(Inputs from PTI)