The Sun reports will tell the FA he did not hear Terry making any racist comments to QPR's Anton Ferdinand.
FA chiefs have launched an investigation into Sunday's stormy West London derby at Loftus Road following an official complaint from QPR.
The Metropolitan Police are also looking into claims that England skipper Terry called Ferdinand a "f****** black c***' during Chelsea's 1-0 defeat.
Chelsea full-back Cole is expected to be called by the FA as a witness to the incident after TV footage showed him walking past Terry at the time of the alleged insult.
But The Sun understands the England star did not hear anything said between the rival defenders.