Hennessey missed the Dragons' Euro2016 opener against Slovakia on Saturday with a back spasm and was replaced by Liverpool's Danny Ward in the 2-1 win but could be back for the Lens clash with the Three Lions.
"Wayne has trained. We lost him just before Slovakia which was disappointing but Danny Ward did a great job," said Wales boss Chris Coleman.
"Wayne feels a lot better but we'll see if he comes through. Hopefully there'll be no reaction in the morning."