There many people who believe that Ganesha might have been a Yaksha earlier. Yaksha are worshipped from the Vedic age and considered as supernatural beings in Hinduism.
In some manuscripts instead of Ganpati the word Vatajakkho is used. Vatajakkho means Yaksha residing in the vata or banyan tree.
There were many elephant-headed Yakshas in ancient literature. Yaksha images with elephant head belonging to Sunga-Kushana period were found at Mathura and Amaravati in South India.
Huge image of Yaksha-Vinayaka of Kashi is very famous. As per Coomaraswamy, pot-bellied Ganesha images imitate similar Yaksha images.