The Blues boss wants his players to respond to the pressure cooker of fighting for silverware in the same manner of two players who have helped him to previous successes.
The Portuguese led the Blues to two Premier League titles in his first spell at the club with Drogba as his attacking linchpin, while Ibrahimovic's goals helped Mourinho storm to the Serie A title in his first season at Inter.
The former Real Madrid manager now wants to see his current Chelsea squad develop a title-winning mentality, insisting that players deal with the pressure of competing at the top in different ways.
"I like to put pressure on them, yes, but you have to analyze the players you're working with," he said. "I gave Didier as an example. When I put real pressure on him, the animal was always coming out. Ibrahimovic at Inter - exactly the same. When I put real pressure on him, I knew that the answer was coming. It depends on the players' profiles. Some react in a very good way. Some don't.
"I have players who have told me not to criticize them in front of the other guys because, 'It's not good for my self esteem'. I've had everything."
The Chelsea boss also wants his players to take the challenge of a title fight as a positive.
"One of the things is to make the pressure of fighting for the title to be something natural, something that players accept in a positive way, not in a negative way. We have here some people who won the title before, but they've not won it for quite a long time. When you don't do that for quite a long time, you forget it.
"We've also got players who were playing in clubs not used to fighting for titles, clubs who'd do fantastic one day and see what would happen the next. That pressure to try and be top of the league, knowing that every little detail and every point can make a difference."