The Blues boss issued his warning as the Premier League club prepared for the first pre-season friendly of the American tour against Club America in California on Saturday.
Chelsea appointed Grant late last week and the former Israel manager flew out with Mourinho and his squad to Los Angeles on Monday.
While the Portuguese coach welcomed the arrival of the man who left his role as technical director at Portsmouth, he made it clear in what areas Grant's input would not be welcomed.
Mourinho said: "I think the club was very clear in the statement they put out. If you want to know more about his work ethic, you'll have to speak with him.
"He's here to give some support to different areas in the club and for me that is not a problem.
"If the club wants to bring people to make the club better and to create a job for somebody to support those different areas in the club then fine.
"From my point of view, he must not interfere with the power I have in relation to my job. So, welcome, and I will try to help him with what happens at a club like Chelsea."
Mourinho said he was waiting to hear on how long he would be without England left-back Wayne Bridge, who injured a hip on international duty at the end of last season.
"Bridge has a problem in his hip he brings from his last game with the national team," Mourinho said.
"Yesterday, he tried to train but it was not feeling good.
"I'm not sure how he is but he is in the medical department's hands and they have to make a good judgment of his situation and then make a decision about his near future."
There was better news on Chelsea's other England left-back, Ashley Cole, whom Mourinho said was set to begin training with the squad in Los Angeles next week.
"Ashley is in the final process of his recovery," his manager explained.
"He was very professional in his holidays, which were just a week because he was working and trying to recover during the whole period.
"We believe he can start working with the team in the US, in the middle of the second week and so we hope he will be ready to play in pre-season matches when we return to Europe and then start the season."
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