The 29-year-old was poised to return to the club just months after being released at the end of the season.
However, an offer of a short-term deal fell through when he failed to prove his fitness during a medical earlier this week.
After receiving a number of jibes, Cole took to social networking website Twitter to post a topless photo of himself showing off his physique.
Fat What? pic.twitter.com/MOvPX9DOm4— Carlton Cole (@CarltonCole1) September 6, 2013
The club is still working with Cole on his fitness.