The Gift of the Givers charity told Swedish Radio News that after a lengthy search, they had word from the militants that both hostages were in good health and a special video had been prepared for collection with more information.
Imtiaz Sooliman, head of the African based charity, said that it had not been easy to track down the kidnappers.
"We finally got a breakthrough several weeks ago. It was not directly but a middle man who knows how to contact them. The video is much more than just proof," he said.
The Gift of the Givers, who are acting as mediators on behalf of the families, released more details on its website.
"Both families are overwhelmed with joy; for three years and eight months they had absolutely no information. With our involvement we made contact with the captors in under four months," it said.
"Our analysis is the following: "someone" agreed to take up our "case", the captors have accepted Gift of the Givers as negotiators on behalf of both hostages, a special video has been prepared for us and they are ready for "dialogue". We now need to get possession of the video and view the contents, then wait for "demands" or instructions on the way forward or any other relevant messages. Depending on the content of the video and us successfully acquiring it we may consider releasing it publicly," the group said on its website.
In autumn, 2011, Johan Gustafsson and a friend embarked on a motorcycle trip from Sweden to South Africa. When Johan Gustafsson came to Timbuktu in Mali, he and two others were kidnapped at a restaurant. Information since has been hard to come by.
On Wednesday, four years to the day when Johan Gustafsson was taken, his sister, Ella Gustafsson, is proud that her family has never given up hope.
She tells Swedish Radio News.
"We carry with us hope. Noone in the family says that it is hopeless. And it makes you strong and feel hopeful," she says.