The Frenchman was impressive in the 3-2 win over Fiorentina on Wednesday where he underlined his undoubted, if inconsistent, potential.
"I have a special relationship with him," the Roma official told Centro Suono Sport.
"He had a tough start to life here, but he just needed to understand his qualities. Mirko Vucinic went through the same thing.
"I liked the character he showed against Fiorentina too. As well as being a great footballer, he is showing the character that is needed for Italian football."
Menez was signed from Monaco in the summer of 2008, but he has infuriated at times with his on and off showings.
"He's one of those players who annoy fans because they make a mess of the simple things, but excite the same supporters with a piece of magic," continued the 1982 World Cup winner.
"Jeremy is working well and it is pleasing to see him demonstrating it on the field of play. He's a better player than I was."