Spurs' fine start to the season has led to suggestions they are genuine Premier League title contenders.
Tottenham are second only to Arsenal in the table after earning 13 points from their opening six matches.
Spurs drew 1-1 with Chelsea on Saturday but arguably looked the better team, with Roberto Soldado, Christian Eriksen and Paulinho all impressing once again.
Holtby insists Tottenham's sights are firmly set on a top-four finish, rather than winning the title for the first time since 1961.
"Everyone can dream but our main aim is to get Champions League football," he said.
"I think we've got the quality and the ability in the whole squad to do that, I'm very confident. It's a long season and everyone has to be at the top level to reach that.
"Chelsea was a big test, absolutely, and I think we're in a good way and playing a wonderful season.
"I think the manager was proud of us and how we committed to the game and how we fight in our game week in and week out. We've had a lot of games now in the last couple of weeks so everyone's just done a fantastic job.
"We have to keep on progressing. It's very early in the season, we have to keep working hard. We've got a couple of games now where we have to get some points and stick up top and defend our place up in the top four."
Holtby himself is having to settle for a place on the bench more often than not.
"I didn't do the best that I can do last season, but I've progressed and now I think I'm getting more involved," said Holtby, who set up three of Tottenham's Capital One Cup goals against Aston Villa in midweek.
"I feel very comfortable and very proud to be here at this club, and I just try to do the things that I do best.
"Roberto Soldado is a fantastic striker. I hope one day I can play behind him and I'm learning Jermain Defoe's runs too.
"It's easy for a number 10 or a central midfielder to put these players in because they make some wonderful movements, and I'm just happy to be here."