Argentina striker Higuain would welcome left-back Cole to Real this summer.
Higuain told The Sun: "At Madrid, Cole's football will make all the headlines, not his private life. I think that will be a big incentive for him.
"I have spoken with a couple of senior players who the club confide in and they are very confident that we will sign him in the next few weeks. Once players have played for Jose Mourinho, they seem to want to follow him. Jose is very much like Argentina coach Diego Maradona in the sense that he will lay down his life for his players.
"It's everybody inside the club versus the rest of the world and that protection which the coach offers is a real incentive. Ashley will know all about Jose's passion and love for his players and I am sure he is keen to link up with him again."
He said: "The vibe around the training ground is that the deal will be done. All the players are very excited about his arrival. It does not surprise me that Chelsea say he is not for sale.
"If you have a player who is the best in the world in his position then you do everything you can to try to keep him.
"But when Madrid want a player we usually get our man.
"I was speaking with Cristiano Ronaldo and he told me Cole is the toughest defender he has ever played against.
"So if Ashley Cole decides he wants to join the greatest club in the world and play for his old friend Jose Mourinho again, then I am sure the transfer will go through before the start of the season."