The 33-year-old has been in and out of Rudi Garcia's starting XI at Stadio Olimpico since joining in the close season and has made eight Serie A appearances so far.
Cole has subsequently been linked with a return to England and Palace manager Neil Warnock stated earlier this week that he would like to bring the former Chelsea man to Selhurst Park.
However, Cole's representative ruled out a switch on Wednesday and Warnock is not confident of doing a deal.
"I do not think there is any chance whatsoever," he said. "The facts are that he is not going to leave Italy for a year.
"He is loving it there. He walks about in the town without getting recognised. The press are not shoving cameras in his face, so he is loving it.
"I was asked the question 'would I like Ashley Cole' and I said: 'Yes, I would love him', but we have already been told that there is no way he is coming back to England."
Cole won every domestic honour and the UEFA Champions League during an eight-year stint at Stamford Bridge.
He also earned two Premier League titles and three FA Cup medals with Arsenal.