You can use the BytesIO class to get a wrapper around strings that behaves like a file. The BytesIO object provides the same interface as a file, but saves the contents just in memory:

import io

with io.BytesIO() as output:
    image.save(output, format="GIF")
    contents = output.getvalue()

You have to explicitly specify the output format with the format parameter, otherwise PIL will raise an error when trying to automatically detect it.

If you loaded the image from a file it has a format parameter that contains the original file format, so in this case you can use format=image.format.

In old Python 2 versions before introduction of the io module you would have used the StringIO module instead.