Is there any possible way to create select attribute with image? For example dropdown list: NEW/SALE/FAV/RATED ... etc and each option with it's own image ?
No either you use
swatches or you use
Drop down.There is no option of using drop-down with images.If you select drop-down then on back-end you won't be able to upload images. There are extensions that enable you to upload images with options and you can use them. Here is the one i found for you. SWMS - Option Image2