You have an image and want to create transparent background but have a fuzzy border.
Just to be sure that the image uses alpha channel, right click on the image Layer->Transparency->Add Alpha Channel
- On top menu of Gimp select Windows->Toolbox
- From the Toolbox select "Fuzzy Select Tool" (magic wand icon)
- Click on the background color so it can be selected and press Esc
- On top menu select Filters->Blur->Gaussian Blur