Ledley was included in Coleman's squad despite fracturing his leg on May 7 and Robson-Kanu has an Achilles problem.
Coleman said it would be "reckless" to start with three players who were not fully fit, but indicated that he was open to bringing them on from the bench.
"I'm not giving anything away to say we can't start with all three. It would be reckless really," he told reporters.
"Joe Ledley did the injury at the end of the season and we were all thinking the same thing -- a broken leg is a broken leg. But he has done so well to get back to where he is.
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"I think it is fair to say you can't really see Joe playing 90 minutes. But can he play a part? Yes.
"He could play a part, both Joes and Hal, unless there is a real bad reaction between now and the weekend."
Liverpool's Allen, whose last competitive fixture was the Europa League final against Sevilla on May 18, was the likeliest to start, because of his importance to how Wales play, the manager said.
"Between now and the end of the season Joe Allen has had more football... so you would have to say Joe is further down the line in terms of being ready to start a game," Coleman added.
"And he is integral to how we want to play because he plays in that pivot role for us."
Wales and Slovakia have been drawn in Group B for the 24-team tournament in France. England and Russia are the other teams in the group.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
