The crew of 72 had been evacuated from the ship on Saturday after a fire broke out on board, according to Spanish media.
At the time, the ship was moored at Las Palmas port on Gran Canaria island, a popular tourist resort.
Fearing the blaze could spread, Spanish authorities towed the boat out to sea. Local media published photos showing a column of black smoke rising from the vessel.
The Oleg Neydenov sank 15 miles (24 kilometres) south of Maspalomas, another town on Gran Canaria, Spanish rescue services said.
The rescuers viewed the wreck on Wednesday to check whether there had been a fuel leak "and to take action if necessary".
Branding the Russian vessel a "pirate ship", environmental organisation Greenpeace said the trawler's tank had a capacity of up to 1,400 tonnes of fuel, sparking concern over possible pollution.
The group discarded however the possibility of a spill similar to the Prestige oil tanker catastrophe of November 2002, which saw 63,000 tonnes of fuel spilt into the Atlantic Ocean off northern Spain.
In January 2014, the Russian trawler had been at the centre of a dispute between Russia and Senegal, which accused the Oleg Neydenov of fishing illegally in Senegalese waters.
Senegal seized the boat for three weeks and then towed it southwards towards the Guinea Bissau border.
The ship's owner, a group based in Murmansk in northwestern Russia, paid Dakar €900,000 ($950,000) to have it returned.