Nonetheless, having been led by Ancelotti for eight seasons, Gattuso is under no illusions that the 49-year-old has the ability to dwarf Mourinho's achievements and help the club win the cup that continues to evade them.
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"Carlo is an expert in the Champions League and that is still something Chelsea are missing, even though they have come close.
"If anybody can guide them to the biggest prize it will be Carlo, there is no one more qualified."
With no doubt his former coach will adapt to the Premier League with ease, the 31-year-old compared Ancelotti's temperament and reputation to that of Manchester United manager Sir Alex Ferguson's.
Should Chelsea players not share their new manager's attitude and way of thinking - they are sure to know about it sooner rather than later according to Gattuso.
"In England Sir Alex Ferguson is famous for his treatment in the dressing room when things are not as he wants and the same is true of Carlo - when he is not happy, you will know about it," said Gattuso.
"If there are any attitudes that do not fit with his way of thinking at Chelsea, they will learn very quickly they need to change their attitude.
"He does it because he knows it is for the good of the team - with Carlo the players are under no doubt who is boss."