Coastguards say the stricken ship Hoegh Osaka has remained in the same position overnight but could be moved on today.
The 51,000-tonne car carrier, which was stranded on the Bramble Bank sandbank, was moved and anchored two miles south-west of Lee-on-the-Solent last night after it came free and began drifting yesterday afternoon.
The Maritime and Coastguard Agency started towing the vessel to a new location at around 4.30pm and a temporary exclusion zone of 300 metres was put around the vessel.
This morning, a spokesman for the MCA said: ‘The idea is just to check it for damage. There was a small hole in the vessel. They have fixed that now.
‘It shouldn’t be too long before they move it on.’
The ship was grounded deliberately after it ran into trouble while sailing from Southampton with its cargo of 1,400 luxury and standard cars as well as 80 pieces of construction equipment.
Sean Woodward, the leader of Fareham Borough Council, says he is terrified that oil will spill from the ship.