Conquering Europe is the minimum requirement for the Special One if he is to be branded a success in his second spell as manager at Stamford Bridge, according to the ex-Blues boss
The self-styled 'Special One' is expected to take up the managerial reins in west London from recently departed interim boss Rafael Benitez after agreeing to end his three-year reign at Real Madrid.
Mourinho transformed the Blues into Premier League title winners during his first stint at the club between 2004 and 2007, but left the club by mutual consent without having claimed silverware in Europe.
"I'm curious to see who's going to come - everyone thinks it's going to be Jose Mourinho," Gullit told the Daily Mail. "I think it's going to be difficult, he has to win a lot of things again like their hearts and their confidence.
"The fans will be happy, that is for sure, but it's a different group of players, everything is different.
"He has to at least win the Champions League, because that is what he always wanted and that is what he is famous for, so that is something which he needs to win.
"He can do it, but can he do it at Chelsea? It's a different ball game also because he is well known for his psychological approach to the players.
"They always want to play for him but it didn't work at Real Madrid and that is something that is his strongest point."