How to use Tailwind CSS with Next.js Image

There’s a discussion and related example over at the Next.js GitHub project. It sounds like that example achieves what you want to do. tl;dr:

<div className="h-64 w-96 relative"> // "relative" is required; adjust sizes to your liking
  <Image
    src={img.img}
    alt="Picture of the author"
    layout="fill" // required
    objectFit="cover" // change to suit your needs
    className="rounded-full" // just an example
  />
</div>

The image will preserve its original aspect ratio and fill / cover (or whatever object-fit you chose) the size of the outer div, which you can set using Tailwind classes. Other styles, like rounded corner, can be applied to the Image.