Salvage operators have been unable to board the grounded trawler, the Fasnet, due to dangerous sea conditions.
The 27-metre French registered fishing vessel ran aground at the mouth to Cuan an Daingin on Sunday after it lost engine power.
Its 14 crew were airlifted from the trawler in dramatic circumstances by the Irish Coast Guard's Rescue 115.
It had been hoped to board the vessel on Monday but weather and sea conditions didn't allow for it.
It is now hoped conditions might improve after the weekend allowing contractors to board.
In a statement issued on Monday, the Department of Agriculture, Food and the Marine said it is continuing to closely monitor the situation but "given the precarious location that the vessel has run aground any attempt to board the vessel is weather and tide permitted".
An Daingean, and the location where the trawler went aground, is managed by An Daingean Fishery Harbour Centre on behalf of the Department.
Within an hour of the vessel going aground on Sunday (11.30am approximately), the Harbour Master enacted the ports emergency plan with a marine salvage operator on site by 2am, and an oil spill response contractor on site by 7am, according to the Department.
A spokesperson said it is monitoring the situation "as it evolves" but so far no-one has been able to board the trawler to carry out salvage and pollution risk assessments.
