The University of Michigan Press annually sponsors The Literary Fiction Award, the prize for which is publication of your novel. It’s a wonderful press that publishes really fine literary fiction. No fees for this contest, either. You do have to have previously published at least one literary novel or story collection in English, though. If you meet that qualification and have a manuscript ready to go, check out the details on The University of Michigan Press website. The deadline is July 1!
If you haven’t published a book yet, but have a fiction manuscript linked the the Great Lakes Region, you might submit to the press’s Sweetwater Fiction series. Best of luck! – Meg