The 31-year-old was an initial injury doubt for the Three Lions' 1-1 draw with France on Monday due to a reported illness. However, the Champions League winner managed to complete 90 minutes in Ukraine.
While Cole did start the training session at England's base in Poland, the defender went on to leave the main group with physio Gary Lewin.
The Football Association have claimed that there is no concern surrounding Cole following his departure from the session. However, it is understood that Martin Kelly was absent from training due to an ongoing virus.