During the hunt, the Swedish military made public a grainy photo of what appeared to be a suspect vessel on the surface of the water.
The military has since been analyzing the photo further and believes the vessel was a small submarine, rather than an underwater vessel used by divers, as some had suggested.
According to the source speaking to Svenska Dagbladet, the analysis revealed part of the main structure of a submarine along with two masts.
The huge military operation evoked memories of the 1980s for many Swedes, who recalled dozens of occasions when the Nordic country's navy was in hot pursuit of suspected Russian submarines.
Last week, Sweden's Foreign Minister Margot Wallström said she was worried about the growing Russian military presence in the Baltic Sea and promised that Sweden would defend its territory.
Her comments came days after a poll suggested more Swedes are now in favour of their country joining Nato than are against the idea.
The suspected submarine incursion ranked as one of the three most high-risk incidents in a report released on Monday on the "dangerous brinkmanship" of close military encounters between Russia and the West in 2014.
The European Leadership Network also pointed to several serious incidents involving Russian fighter jets near Sweden's coast as evidence of escalating tensions in the Baltic Sea region.
In March, a Scandinavian Airlines plane carrying 132 passengers came within 90 metres of a Russian surveillance aircraft that had not transmitted its position.
"A collision was apparently avoided thanks only to good visibility and the alertness of the passenger plane pilots," the report said.