The Coastguard has been assisting the Russian-flagged vessel which has a significant list, meaning it is leaning to one side.
It had been anchored in the Solent with a pilot boat assessing its stability and cargo.
In an update on its Facebook page, the Maritime and Coastguard Agency said: ‘Plans are now underway for the Russian flagged vessel Mekhanik Yartsdev to be taken to a berth in Southampton Harbour.
‘The vessel has its own power and as a precautionary measure it will be assisted by a pilot vessel, two tugs and escorted by an RNLI all-weather lifeboat until it’s safely alongside.
‘Once berthed a surveyor will inspect the vessel’s stability and cargo.’
The 13 crew onboard are reported to be safe and well.
The Coastguard is issuing navigational safety broadcasts every 30 minutes to warn shipping in the area.