Ranatunga, 44, who is a ruling party legislator, could take over as early as Friday when parliament meets for a crucial vote on President Mahinda Rajapakse's budget for 2008.
Ranatunga was regarded as one of the disgruntled legislators who wanted to oppose the budget at the first vote on November 19, but was persuaded by his father, a senior member of the ruling party, to vote in favour of it.
A top sports ministry official confirmed the move to appoint Ranatunga as the country's cricket chief was being discussed.
"The move is being currently discussed, although there is no finality on the issue," sports ministry's Kapila Bamunuarachchi told AFP.
Ranatunga became a legendary figure in Sri Lanka after leading the squad to their lone World Cup triumph in 1996.
He has been critical of the current cricket administration and blames it for the dwindling of Sri Lanka's talent and reserve stock to replace the ageing national team.
Ranatunga played 93 Tests and 269 one-day internatio