There is not an abundance of criticism available for A Possible World; however, the small amount accumulated so far has been positive. In an article for Booklist, critic Donna Seaman describes Koch's final effort as "a beautiful new collection" from "a key figure in American poetry." Seaman singles out one of the lengthier poems, "A Memoir," for particular praise that could be applied to Koch's work as a whole: "Wryly and affectionately reflective, teasingly subversive, and still vitally curious and joyfully creative." In a review of A Possible World for Publishers Weekly, one critic observes that the various writings in the book "display Koch's verve and light touch, but are unmistakably colored by requiem."

Throughout Koch's career, critics have applauded the poet's sense of humor and his willingness to write "unpoetic" poetry. Critic Ben Howard writes in a review of Koch's Straits for Poetry, "in his...