The left-back, who picked up the injury in training, is expected to learn the extent of the damage later this week.
"He is still feeling pain in the base of his foot so we have sent him for a scan to assess the extent of the damage," Davis told the club's official website.
"We thought the pain would have gone by now, but it hasn't and we want to make sure he is right. We want to be reassured with him, to make sure it is nothing too serious.
"He is improving all the time so we don't think there is anything serious, but it will give us and him peace of mind."
The 23-year-old came through the Crewe youth system.