Some key sources of information, plus some presses to check out
There are some presses (mostly American) listed on The John Fox website: https://thejohnfox.com/publishers-of-short-story-collections/ and https://thejohnfox.com/2017/09/30-best-small-indie-literary-publishers/
An article from LinkedIn from 2017, that lists small presses looking for short stories: https://www.linkedin.com/pulse/17-publishers-accepting-unagented-short-story-erica-verrillo
As literary magazines are sometimes associated with presses that also publish collections, check out this extensive list of magazines that take short stories from Christopher Fielden’s blog: https://www.christopherfielden.com/short-story-tips-and-writing-advice/short-story-magazines.php
The New Pages list of Independent Book Publishers is at https://www.newpages.com/books/publishers
Another way to find small presses is to check out the attendees at a small publishers’ fair. Here’s the London-based event: http://smallpublishersfair.co.uk/
Or to attend a writing conference, and keep your eyes peeled. Here’s a list for conferences and events in North America, for example: http://www.independentpublisher.com/events.php
For writers in the UK, the Mslexia Indie Press Guide will give you a comprehensive list of independent presses.
For the North American market, take a look at the Novel and Short Story Writer’s Market.
And Other Stories
Comma Press
Cultured Llama
Galley Beggar
Seren
Unthank Books
Thresholds Short Story Forum is worth a look, especially if you’re UK-based although the website and forum are no longer updated so are out of date.
http://thresholds.chi.ac.uk/literary-magazines-and-other-markets/
There are some short story presses listed here (though some are out of date): http://thresholds.chi.ac.uk/agents/
Let me know how you get on.
Happy writing,
xx Louise