Stricken Solent ship: Hoegh Osaka could be moved by Wednesday
Plans are "progressing well" to move the Hoegh Osaka from a point in the Solent to Southampton by Thursday.
The vessel is being secured by tugs off Lee-on-the-Solent and is now listing at 47 degrees.
A Maritime and Coastguard Agency spokesman said: "The weather has been favourable and is forecast to remain so, although the salvors are still working in challenging conditions".
More than 800 tonnes of water in the hull has been pumped out.
The salvage team is preparing to pump water out of the car decks and into the empty fuel tanks on the ship.
Salvors plan to move the ship to Southampton Port late on Wednesday or early on Thursday.
Work to pump the excess water from the vessel's lower car deck began on Saturday.
The 51,000-tonne ship, carrying 1,400 cars and 105 pieces of construction equipment, was beached deliberately on Bramble Bank sandbank on 3 January after it began listing as it left Southampton.
It floated free from the sandbank on the high tide on 7 January and was towed to deeper water where it remains.
On 11 January one of the tugs helping to keep the ship in place collided with the Singapore-registered transporter in high winds.