The Portuguese has returned to Stamford Bridge for a second spell - following a trophy-laden stint between 2004 and 2007 during which Terry lifted two Premier League titles, two League Cups and one FA Cup.
The pair have previously revealed they enjoy a close relationship on and off the pitch, but Mourinho stressed the importance of being professional when the time calls for it - calling any selection decision purely "business".
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"I need to be honest with everybody and I think he appreciates that. We spoke about it and he understands perfectly that, as we say in Portugal, 'friends are friends, but business is separate'. This is a kind of business. So yes, he has to prove [himself].
"I cannot make him become protected or favourite in front of someone else, and he knows that because he knows my nature. One of the things I taught them is, in football, you have to prove yourself every day and every week."
Terry struggled to assert himself in the first-team squad last season under interim manager Rafael Benitez following a knee injury, but Mourinho has dismissed suggestions the former England skipper is now unable to perform at the highest level.
He said: "I trust him completely. I know he's a very good player, but he has to prove himself like everybody else. I feel his motivation is there, the pleasure of training and playing is there, his class is there. He needs to work hard and not have injuries. For me, that's the key point for John."