Fox has caught the eye of a number of Premier League clubs with his performances for the Sky Blues this season, with Newcastle having a bid for the 23-year-old turned down in January.
But the former Walsall defender has been left out of Stuart Pearce's 23-man squad for the finals next month.
Coleman told the Coventry Telegraph: "I think he had a very good season and was very consistent and, for me, did more than enough to get in.
"But I don't pick the squad and I would never try to tell Stuart who to pick.
"I just hope that our poor form, as a team, over the last few months of the season didn't have a bearing on any decision."