Manchester City's De Bruyne fractured his nose and left eye socket in a clash with Chelsea's Antonio Rudiger during Saturday's Champions League final.
Belgium's first game is against Russia on 12 June, before they face Denmark (17 June) and Finland (21 June).
"I've spoken to Kevin and he was quite positive," said Martinez.
"We've got to be very cautious, but we will get more clarity in the next days.
"We don't know if we can use him in the first game. I cannot give an answer because I don't have any medical facts right now, we are still assessing the injury and over the next four to five days we expect clarity.
"We are very fortunate that even though he has a double fracture, he doesn't need surgery. An operation would have made it impossible for him to play in the European Championship."
The 29-year-old Manchester City midfielder tweeted he "felt OK now" on Sunday, with Martinez saying he had undergone a number of hospital tests and had returned to Manchester, and would join up with the squad next week as planned.
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