The former Liverpool stalwart and New England head coach says "MLS does not want" the 33-year-old former Arsenal and Chelsea player.
The left back, who signed for Serie A club AS Roma this summer after eight seasons with Chelsea, had told his new club's official channel "I have had other offers from USA, but I didn't want to sit on the beach yet."
Nicol, who played for Liverpool for 13 years and coached the New England Revolution from 2002 to 2011, took exception to the comment.
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"Ashley cole said if I wanted an easy ride I would have gone to MLS. Such an ignorant comment. MLS does not want you thanks," tweeted the 52-year-old, who won the 1983-84 European Cup and five league titles in his playing days.
In a later reply, Nicol subsequently tweeted, "he was good but he ain't as good as he thinks he is" in reference to Cole.
Had Cole signed with MLS, he would have joined former teammates Thierry Henry, of the New York Red Bulls, and Frank Lampard, who is set to sign for New York City.