The Blues manager wants him to keep the club's No.1 on his toes and enthuses about Andre Schurrle and Marco van Ginkel.
The 40-year-old Australian penned a one-year contract at Stamford Bridge after leaving Fulham this summer, restoring the goalkeeping ranks following the departures of Ross Turnbull and Hilario.
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"He is the best in the world, with deference to all the others, and Mark knows that he comes to be an important member of the squad, to compete with Petr and to give us in that position what we have in any other position where we have competition and options, giving protection to each other.
"With Mark we have a goalkeeper who has played an incredible number of matches in the last 10 years in the Premier League and he is more than ready for this."
The Portuguese is also enthusiastic about the Blues’ other two captures so far this summer, forward Andre Schurrle and midfielder Marco van Ginkel.
"Schurrle is still so young but he already has great history because he plays in his national team, he has played Champions League and he played three complete seasons for Leverkusen," Mourinho added.
"So he is a player who is absolutely ready and he gives us more than one position in attack and adds quality. He will be important for us.
"Marco van Ginkel is one of the best prospects. He is not yet like Schurrle - close to being a finished product - but he is a player with great potential.
"Of course he needs to play and he will because he is a player with great potential and, physically, he is more than ready. He is a natural athlete.
"By the technical and the tactical point of view, of course, he is a kid, he has to learn, but I think he is very open-minded and we analyzed him for quite a long time. The Chelsea scouting department did it for quite a long time and I did it in the last five or six months, and we made a collective decision to bring the kid here."