Korg is ‘basket’, Old Swedish korgher. Probably via Danish (Modern Danish kurv) via Low German korf (Modern German Korb) from Latin corbis with the same meaning. Also, from the Late Latin diminutive corbicula comes French corbeille.
Didn't find any info about English basket.
The squirrel found it today… He is happily munching sunflower seeds. More about him here.