The two sides meet at Stadio Olimpico in Rome on Thursday locked at 1-1 following last week's semi-final first-leg stalemate at King Power Stadium.
Lorenzo Pellegrini gave the Serie A side the lead in the East Midlands before an Ademola Lookman equaliser brought Brendan Rodgers' men level on the night.
It leaves the second leg delicately poised but with the Romans on course to end a 14-year trophy drought - if they can first book their place in the final at Arena Kombetare in Tirana on Wednesday 25 May.
Roma are currently fifth in the Italian top flight and their last silverware came in 2008 when winning the Coppa Italia.
Exactly 12 months ago to the day of his appointment, Mourinho, who replaced Paolo Fonseca, says his players are highly motivated.
He said: "I'm enjoying it very much. I'm happy every day I come to the training ground. Do I want more? Yes I want more. Do I want next season to be able to think bigger? Yes.
"I knew the project, the nature of it and I am loving sharing every day with the players."
The former Manchester United, Chelsea and Tottenham manager, who will be without the injured Henrikh Mkhitaryan for the second leg, says the club's supporters have waited too long for a return to former glories and the current crop of players are keen to end the season on a high.
He told reporters: "They want to grow up, I'm with them, I try to give everything I have. The work has been so hard for all of us, I think we deserve to end the season with something to celebrate.
"A trophy would be amazing, of course to finish in a position to allow us to play European competition next season is also a positive thing. Tomorrow is one big step."