Television cameras caught pictures of Mieries leaving a clash with Cole with blood on his fingers during the champions' 32-15 win at Welford Road.
With Mieries apparently not reporting the incident to the referee or director of rugby Dean Ryan, Cole will now have to wait to find out if he will be cited for the incident.
Former Leicester player Austin Healey suggested any bite would have been an accident, commenting: "You don't put your fingers in a dog's mouth."
However, former England winger Jon Sleightholme took a different viewpoint by writing on Twitter: "It's ok for Dan Cole to bite Mieres as he had his hand in his mouth, blood streaming down his fingers. Has to be banned in my view. #unacceptable".
Should Cole face punishment for the bite, then he could miss England's opening international against Australia on November 2.