Mourinho matched former Manchester United boss Ferguson with 106 victories in the Champions League and Europa League when he led Roma past HJK 2-1 in the Europa League last month.
Only Carlo Ancelotti has more victories (120), with the era dating back to the Champions League's introduction in 1992.
Ferguson and Mourinho had a tense rivalry during the Scot's latter days at Old Trafford, spawning from the Portuguese's breakout stint at Porto before regularly locking horns during his first spell at Chelsea.
The Portuguese, who led the Italian club to Conference League glory last season, can surpass the former Manchester United manager when Roma take on Real Betis in the Europa League on Friday (AEDT).
"It's not an extra motivation," Mourinho said. "I am proud of the 106, and when the 107th arrives, either tomorrow or next week, I don't know, but when it comes it'll be a proud moment in my career.
"I've always said that I'll think about this kind of thing when I finish my career. When I finish my career I have so many things to think about and remember, but at this moment, no.
"Right now, the only thing that I am worried about is winning the next game, I'm always [thinking about] the next one and the next one is tomorrow.
"As I said before, it will certainly be difficult, it is a high-level game, very high. But there's no such thing as winning one more game than Sir Alex.
"This is not [why I want to win]. I want to win because we need to."
Mourinho has won 85 Champions League games and 21 Europa League games, compared to Ferguson's 105 wins in Europe's top club competition along with one UEFA Cup (Europa League) victory.
The former Inter, Real Madrid and Porto boss has two Champions League titles and two Europa League titles to his name, the latter with United. Ferguson, who retired in 2013, lifted the Champions League three times.
Ancelotti, who has won the Champions League four times, moved to 103 Champions League wins with Madrid's 2-1 triumph over Shakhtar Donetsk, while he has 13 Europa League wins too.