Some fans have claimed that Cole is past his best, while the 32-year-old has been linked with a move to the MLS in recent weeks.
However, Cole has issued a defiant statement on Twitter, insisting that he is not over the hill yet.
He wrote: "7 FA Cups, 3 league titles, an undefeated season. I'm still not done. #niketiempo @nikefootball."
His tweet was accompanied by a image, which included a photo of Cole, Nike's logo and the words "WHO YOU CALLING DONE?"
Cole has a long-running and lucrative contract with Nike and he wore a pair of personalised Tiempo boots during England's 2-1 friendly win over Brazil in February, a game in which he won his 100th senior international cap.