The Dutch winger, who has yet to sign an extension to his current deal with the Blues, has been repeatedly linked with a move to the Spanish champions and the arrival of Florent Malouda at Stamford Bridge earlier this month has intensified speculation.
But Robben, 23, played 45 minutes in the 1-0 victory over Suwon Bluewings at the Home Depot Center in Carson, California, on Tuesday night as Chelsea continued their winning start to the pre-season with a solitary Didier Drogba strike.
After the match Mourinho said: "The latest with Robben is that he played the game. I cannot tell you more than that.
"At the moment he is a Chelsea player with two more years of contract and he is working well.
"For me, he is a player like (John) Terry or (Frank) Lampard with two more years of contract.
"I look at him as a Chelsea player and he has to compete against very good wingers like we have. I am happy with the situation."
But Real Madrid president Ramon Calderon insists he remains optimistic about signing Robben and told Spanish radio station Onda Cero: "It is a negotiation which will take place in the coming days or weeks and if the situation is favourable, by which I mean financially, I think that he is a player who could be brought in."
All three players mentioned by the Portuguese - Robben and England pair Terry and Lampard - are currently negotiating new deals and Mourinho insisted the Blues would go all out to retain their services.
"The club wants to keep the players, to do everything. I trust the board and (chief executive) Peter Kenyon in the negotiations he is doing.
"I know the players want to stay. I want the players and would be happy if they signed new contracts.
"The club have the right to say 'this is our limit'. The players have the right to say 'if I don't like the contract I don't sign it'. I have no problems with the club, I have no problems with the players.
"As a coach, I just think if they have a contract then they are Chelsea players and I look at them the same as a player with five or six years contract.
"I keep saying, I play the players who deserve it more. Of course, I would love the club to sign a new contract with them but I have no problem with that. I am with the club and the players. I have to be independent in this situation and be honest with them both."
Vi bruger cookies for at kunne give dig den bedste oplevelse. Ved at bruge vores side accepterer du brugen af cookies. Du kan læse mere i vores persondatapolitik.