Speculation is rife at a bust-up between the two following Crespo's absence from the squad that went to Manchester United on Saturday.
Crespo, 30, said from his base with the Argentina squad to face England on Saturday: "There is no way we have fallen out. No way. We didn't have an argument, definitely not. That did not happen.
"I want to stay at Chelsea. You must not believe I will leave in January.
"Mourinho is one of the great managers in the world. He is a good, good person and I am very happy to work with him and our relationship is good.
"I am very happy there. The group of players is great and the manager is great."
"People think that if you sit on the bench you will not have a lot of patience. But I do have patience.
"If I have five, 10 or 90 minutes, I will always do my best. There is no problem with that.
"Am I frustrated? No. I know that I am at Chelsea.
"If I want to play for a small team then I will always get 90 minutes but when you play at a great team like Chelsea you need to be patient. The season is still early."
Yeah, we believe you Hernan.