Spurs currently sit behind Manchester United, Manchester City and reigning European champions Chelsea in fourth spot after accruing 48 points from their opening 26 league games.
Lloris, 26, moved to White Hart Lane in the summer after a four-year spell with Spurs' upcoming Europa League opponents Lyon.
Now he is part of Andre Villas-Boas' Champions League-chasing squad and Lloris told French radio station RTL he believes Spurs are getting closer to the teams above them in the table.
"Today, there's United, City and Chelsea who are a cut above, and who have more financial means. But Tottenham is just behind," he said.
"The club has been trying to establish itself in the top four for some years now."
The table certainly suggests Spurs are close to their London rivals Chelsea, with just one point separating the two clubs.
Lloris has been pleased with the start to the season but is also wary of the threat from other teams currently outside of the top four.
He said: "For the minute, the season has been promising, but the hardest part is yet to come because there are still a number of key matches to be played and we'll have to be ready for that.
"For the moment, we're well-placed, though we're not beyond a possible charge by Arsenal."
Lloris had to be patient after initially making the move to England due to Villas-Boas keeping faith with Brad Friedel.
Now established as the first-choice goalkeeper at Spurs, Lloris reckons the experience of challenging Friedel for the position has made him stronger.
"Things were very clear, that I was coming to Tottenham as the number one," he said.
"But the manager made a decision at the start, and then made a different one a few weeks later. The negotiations over the move were with the chairman, but it was also the choice of the coach. I also had talks with him during that time.
"It's not easy, because I came in after the start of the season, and he was already under pressure because the results were not good at that point in time. It's the sort of situation which helps you grow, it's a personal challenge."