The move follows the deployment of an international military operation to prevent attacks on commercial ships by Yemen’s Houthi rebels.
Several firms have paused shipments via the Red Sea following the attacks.
German shipping firm Hapag-Lloyd has said it will decide on Wednesday whether to resume using the route.
The Red Sea is one of the world’s most important routes for oil and liquefied natural gas shipments, as well as for consumer goods.
It is bookended by the Bab al-Mandab Strait, also known as the Gate of Tears, in the south, near the coast of Yemen, and the Suez Canal in the north.
The Houthis have declared their backing for Hamas in its war with the Israelis, and the rebels based in Yemen have said they are targeting vessels that they believe are heading for Israel. Some ships have come under attack from drones and rockets.
The alternative route, around the Cape of Good Hope, adds about 3,500 nautical miles to the journey. This has led to fears of disruption to the supply of goods transported through the Suez Canal and an increase in prices to cover the higher transport costs.
The news that shipping companies were avoiding the Red Sea route led the US to launch an international naval operation – named Operation Prosperity Guardian – to protect ships.
In a statement issued on Sunday, Maersk said that with this initiative under way, “we are preparing to allow for vessels to resume transit through the Red Sea both eastbound and westbound.”.
“We are currently working on plans for the first vessels to make the transit and for this to happen as soon as operationally possible.”