An online statement says police "are working intensively" to confirm the items are genuine.
Thieves took two crowns and an orb belonging to one of Sweden's 17th Century monarchs before making off by speedboat on a nearby lake.
Local media reports suggest the funeral regalia was found on top of a rubbish bin in a Stockholm suburb.
"All indications are that Karl IX's stolen funeral regalia have been found in the Stockholm area," the statement says, with authorities striving "100%" to identify them.
The thieves ran into Strängnäs cathedral, west of Stockholm, to grab the jewels.
A 22-year-old man is currently on trial for the theft, but authorities are still looking for "additional perpetrators", the statement says.
The items are adorned with pearls, precious stones and gold, and come from the 1611 funeral reglaia of Karl IX and Queen Christina.
A police spokesperson at the time described them as "invaluable items of national interest".
