Sachs was prominent in the anti-apartheid struggle and lost an eye and an arm while in exile in neighbouring Mozambique in a bomb attack by apartheid security forces. A keen cricket fan, he now sits on South Africa's Constitutional Court.
World Cup organisers refused on Thursday to move England's February 13 game from Harare, despite the team's concerns over political and social unrest in Zimbabwe.
If England lose their appeal, they could forfeit the Harare match -- and the four points on offer -- and face demands for millions of dollars of compensation, thus leaving them with a difficult task to reach the second round of the competition.
"The process for conducting the appeal hearing will be left to the discretion of Justice Sachs," the ICC said in a statement.
"This could be based solely on the papers and transcript from Thursday's meeting (of the World Cup technical committee), or involve further submissions from both the ECB (England and Wales Cricket Board) and ZCU (Zimbabwe Cricket Union).
"The Commissioner (Sachs)
Should the judge side with England, however, Zimbabwe, who have already said they will not play if their home matches are moved away, would retain their own right of appeal.
ICC chief executive Malcolm Speed said after Thursday's meeting that England's argument was based in part on "hearsay, radio reports, newspaper reports", adding that police security for the match in Zimbabwe had been increased in the last week.
"It's a very comprehensive security plan around the players and officials," he said.
The Zimbabwe issue has simmered since December when British ministers urged the England team to boycott the Group A match.
Britain accuses Zimbabwean President Robert Mugabe of rigging his re-election last year and compounding food shortages affecting half the population by seizing white-owned farms.