Lloris recently celebrated a decade of service at Spurs and despite being a model of consistency during his 10 years in north London, he is yet to win a trophy there.
The closest the France international and many of his current team-mates came to success was three years ago when Tottenham lost to Liverpool in the Champions League final.
After two seasons away, Spurs are back in Europe's elite competition following an excellent second half of the 2021-22 campaign under Conte, who saw them recruit wisely in the summer to fuel talk the club's trophy drought - which now stands at 14 years - could soon come to an end.
Lloris said: "Yes, I'm still looking for it (a trophy) and I believe we are capable to make it, but as I said its going to demand a lot of effort, a lot of work.
"I feel and believe we are going in the right direction but we know there are a lot of competitive clubs in England and in Europe, so that's why we need to go step by step.
"But the belief is there, that's the most important and we feel that we are ready to compete.
"We feel that we are improving but we know it's never enough. You always have to push and improve yourself and go over your limits if you want to arrive and to succeed."
The appointment of Conte last November has transformed Spurs following an indifferent period where Mauricio Pochettino left, Jose Mourinho arrived and briefly impressed before being fired on the eve of the 2021 Carabao Cup final while his replacement Nuno Espirito Santo lasted barely five months.
After winning the Premier League and Serie A, in addition to numerous domestic cups in his managerial career, Conte is in no mood to see Tottenham simply make up the numbers.
Lloris feels the squad are beginning to resemble the image of their serial winning boss.
"Obviously our manager is our main leader and I believe that there is a connection between a manager's feelings and the way the team is playing. At the moment I feel a great connection but it's not the moment to do less," the 35-year-old insisted.
"It's the moment to do more, to push ourselves, continue in the right way and let's see where we will be at the end. As I said before, we are only focused on the game.
"I don't really like to talk about the past. I'm more focused on the present. It's the story of a club. There are ups and downs.
"When you face difficulties it's about how you bounce back. I believe the club is going in the right direction with the help of Antonio Conte and his coaching staff, but we know there is still a gap for improvement.
"It's a new adventure for the club. It's been two years now without this competition and we're all excited to be part of it, but also we have to play with ambition."
Having progressed through the Nice academy system and played for the Ligue 1 club for three seasons, the fixture against Marseille carries extra significance for Lloris.
He added: "It's a kind of derby in the south of France, but it's a long time ago for me! When you play in France, every time you face Marseille it's always a big game.
"They are one of the biggest French clubs, especially in European history. It's a special place. Whether you are French or you play for a French team, facing Marseille is always very special."