Inter captain Handanovic joined from Udinese in 2012 but is yet to lift any silverware during his time at San Siro.
The Nerazzurri looked like early contenders for the Serie A title this season but lost ground to Juventus and Lazio before the coronavirus outbreak brought play to a halt and they are nine points off top with a game in hand.
Asked for his recollections of Inter's 2-1 win over Empoli on the final day of 2018-19 that secured Champions League qualification ahead of local rivals Milan during a video chat on the club's social media channels, Handanovic said: "It was a great evening. It went well which is what mattered most. It was a tough moment. It was all in one night. It was all riding on that game.
"It was an exciting and great night. We enjoyed it. It is nice to look back at that game, of course. It's nice to think about it, but you cannot live off memories."
He added: "Joining Inter is a dream for every player. Every ambitious player aims for the top. Inter back then was the top club in Europe, in the world. It was an amazing joy, I was very proud. It was also a big personal challenge. It was like a dream.
"[My dream now is] to lift trophies with Inter."
The suspension of Serie A is expected to be extended beyond the initial return date of April 3, with Italy's minister for sport Vincenzo Spadafora suggesting a resumption of play one month later was "too optimistic".
"Everyone is aware of what is going on. We're following the rules, staying at home and doing what we're being told to do. Obviously, there's a bit of worry, but this is normal," said Handanovic.
"It's difficult to stay focused, but we're training at home. We're also watching old videos or matches on TV and staying in touch. As is also the case with many other teams, videos have been sent by the coaches so we can continue to train.
"Aside from this, I'm with my family and have been playing cards and chess. I've also been doing some reading and watching TV in the evening with my children."