It has been talking for years about privatising these and other companies, but has repeatedly postponed the sales.
The central bank also said last week it had selected two banks to advise on the sale of its 99.9% stake in United Bank, a deal it said several years ago would occur by end-2016.
Economists say if these and other sales do go through it would be a sign that Egypt, after enacting painful macroeconomic reforms backed by the International Monetary Fund (IMF), is serious about opening up the economy.
"The government has managed to restore macro stability, it has reined in the budget deficit, monetary policy has improved, the pound has been devalued and inflation is now coming under control," said Jason Tuvey, senior emerging markets economist at Capital Economics.
But he said Egypt had so far shied away from privatisations and other structural reforms that could keep growth at the 6% economists say is needed to absorb hundreds of thousands of new workers entering the market each year.
"The fact that they're continuously being delayed suggests that there is significant resistance from within the regime towards the government ceding control," Tuvey said.
Egypt hopes the sales will bring in revenue, encourage investment and help its bourse, whose market capitalisation of $40 billion is less than a tenth of the Saudi bourse and smaller than even Casablanca's in Morocco.
Boosting investment has taken on extra urgency since small protests broke out last month over economic grievances.
"The government's macroeconomic policy, under the IMF ($12 billion) loan, has been widely lauded by investors. But its microeconomic, structural reforms, such as improving the ease of doing business... matter too," said Hasnain Malik, head of equity strategy at Tellimer.
Charlie Robertson, Renaissance Capital's global chief economist, said privatisations were "tremendously helpful" to provide more variety on the bourse.
The government announced a list of 23 companies in March 2018 for partial sale that year and in early 2019, but the 2018 emerging market crisis derailed the plan.
The risk of a global downturn may deter officials, who fear being accused of selling state assets at below their true value, an accusation prosecutors leveled at officials close to Hosni Mubaral after the 2011 uprising, an Egyptian economist said.
Other impediments include bureaucratic obstacles, economists said.
"There might be some people not happy with the share sales and putting up hurdles, including the legalities," said one Egyptian asset manager, asking not to be named.
So far the only sale in over a decade was of a 4.5% stake in tobacco monopoly Eastern Company EAST.CA , which went for 1.7 billion Egyptian pounds ($100 million) in March.
Investment bankers working on Alexandria Container have taken the proposed sale to select investors outside Egypt for market testing, but since then there has been no update, a source familiar with the transaction said.
"The exact timing will be determined by several factors. We're still waiting for more clarity," he said.
Public Enterprise Minister Hisham Tawfik put the delays down to "purely legal" issues, including the death of one of the judges working on the case.
"The investment banks who are managing the two next offerings are ready and have done their road shows and are ready for the offerings as soon as this problem is over," Tawfik told CNBC Arabia television on Sunday.
Finance Minister Mohamed Maait said it was crucial to take the sales to investors at the right time.
"We will not go to the market unless we are sure this is a good decision, we will get a good outcome, with results. Otherwise, we will have to wait. We are not in a hurry," he told Reuters last month.
(additional reporting by Ulf Laessing, Karin Strohecker and Tom Arnold; Editing by Ulf Laessing and Emelia Sithole-Matarise) ((email@example.com;))