Terry stated after Tuesday night's 1-1 draw at Paris St Germain that he would like to extend his stay at Stamford Bridge knowing that club policy is to only grant single season deals to players over 30.
Mourinho insists the 34-year-old's form points towards another campaign with the Barclays Premier League leaders.
"Everyone wants to stay at Chelsea, especially John Terry because he has been here all of his life," Mourinho said.
"He accepts our policy on players over 30 with a smile and accepts it as a challenge
Last season he won the challenge by performing so well and getting the one-year extension.
"This season he is winning the challenge and the right to have another one-year extension
It's what John wants, it's what the club wants."
Mourinho has two years left on his contract and is unwilling to discuss his future beyond stating he is content at Stamford Bridge.
"I want to stay
I think the club is happy
I'm not waiting for offers
I'm not going to give any space for speculation or for interest from other clubs," he said.
"I want to stay, I don't want to go
My story is a non-story because I will stay for as long as (club owner) Mr (Roman) Abramovich wants me."
Among the talking points from Chelsea's draw in Paris was the brutal attention playmaker Eden Hazard received at the hands of PSG.
"Hazard is a lucky boy not to be injured
During the game I was aware of the number of fouls, I was counting and I was aware that every time he had the ball he was surrounded and fouled," Mourinho said.
"But only on TV afterwards could I understand the dimension of the fouls because some of them were really, really dangerous ones.
"He's a lucky kid, but he deserves luck because he's so fair and honest that he deserves to be lucky.
"He's loyal, he enjoys his game and is not the type of player who when he is winning performs tricks to provoke people and create emotional reactions.
"I'm proud of him for being honest on the pitch and I leave it with the authorities to do something about the rest."
Source : PA
Source: PA