The Portuguese, who led the Blues to successive Premier League titles in 2005 and 2006, has returned to west London after the departure of Rafa Benitez, the former Liverpool boss who failed to win over many of the Chelsea faithful. (Agencies)
"I want them to be with us as a Blue family - a Blue family that last year, at certain moments, looked like it was broken," he said in an interview with British newspaper The Sun published on Friday.
"I just want to put the family back together so I want them to support us all. I want the players to be supported, I want them to support Chelsea. I want them to be with us in good moments and bad moments, in cold weather and sunny weather, at home and away, when we are winning and losing,"
Benitez's time at Stamford Bridge was marked by fan hostility after his appointment last November in place of terrace hero Roberto Di Matteo who had led the club to Champions League glory earlier that year.
Having won an FA Cup and two League Cups along with those two league titles, Mourinho has much to live up to in his second spell at the London club but says he is not jeopardizing his reputation by having another stab at the job.
"I don't think I'm risking my legacy here. What you did, you did. No one can delete it, no one can take away my history at Chelsea," he said.
"And I know the Chelsea mentality. They will never forget what I did before. They will never forget that I gave everything to this club," he added.
He does, however, want to look to the future rather than the past. "I want to be seen as the new manager of Chelsea. I want to be analyzed for what I do now. I want to work here and be loved for what I do now," he said.
Chelsea open their Premier League campaign at home to promoted Hull City on Sunday.
The Portuguese, who led the Blues to successive Premier League titles in 2005 and 2006, has returned to west London after the departure of Rafa Benitez, the former Liverpool boss who failed to win over many of the Chelsea faithful.