French emergency teams were on standby on Monday, according to regional paper Ouest-France, as a four-man team from the Dutch Smit Salvage company tried to attack a tow line to the 164-metre-long Panama-registered ship, which is lying at a 40-50° angle in the Bay of Biscay.
The team landed on the ship on Saturday and attached a tow line between the Modern Express and a tug but it snapped because of the rough seas.
Strong winds and waves of nearly six metres prevented salvage attempts on Sunday but the winds slowed to 15-20 knots on Monday, allowing a new attempt to be made.
If they fail it is expected to hit the coast between Bordeaux and Bayonne at any time between Monday night and Tuesday night.
An emergency anti-pollution plan will be put into operation if that happens, although the ship had only 300 tonnes of fuel in its tanks, compared to the 77,000 on board the Prestige, whose shipwreck in 2002 caused an environmental disaster.
The Modern Express's 22-strong Filipino crew was airlifted to safety by Spanish helicopters last week after it capsized on Tuesday off the coast of Spain.
It was travelling from Gabon to the French port of Le Havre.