The experienced Hennessey was ruled out of the group B opener against Slovakia on Saturday after a back spasm in training the day before the match, opening the door for 22-year-old Danny Ward who only made his international debut in March.
Hennessey has not trained since picking up his injury but Coleman is confident he can make a comeback for the showdown with England.
"He hasn't trained since before we lost him against Slovakia but he will today," Coleman told journalists on Wednesday. "Let's see if he can get through the session.
"He feels a lot better and I think he will. I'm hopeful there'll be no reaction tomorrow."
Hennessey shone during Wales' qualification, conceding just four goals and keeping seven clean sheets in 10 matches, but Ward impressed against Slovakia, making a series of fine stops after a slightly nervy start to the match.
(Reporting by Ed Dove; Editing by Ian Chadband)
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