Cole was carried off the field and into the dressing room during the 3-0 win over Estonia with an ankle injury.
"He rocked his ankle blocking a shot," said England head coach Steve McClaren.
"It doesn't look good but injuries can settle down in 24 hours and it is a critical period. We will know more on Sunday evening when we reassemble."
McClaren added after the game at Wembley: "They have X-ray machines here so we are waiting for the results."