"The objective is to try to stay there for as long as possible," Aurier told RMC Sport. "We are very happy about what is going on and our position because we deserve to be top of the table. And I can't forget that we dropped some points stupidly at home against West Ham or Newcastle.
"However, I think it is too early to think about the title. We can't rush anything. A couple of weeks ago, Southampton were top of the table and then it was Leicester. Now it is us.
"We are trying to do better than last season. We didn't start well in the last campaign. It is much better already this season. We just want to be in the conversation and we are. We have big games coming up and we want more results like against Manchester City and we will continue to fight for the challenges to come."
With Jose Mourinho recently celebrating a year in charge of the club, Aurier, who is now in his fourth season with Tottenham, senses that they're on the cusp of achieving major success.
"Of course, I can feel there is something special happening here," he said. "I am not a dreamer; I take things as they happen but today, we can be proud of ourselves for the start of the season that we have had.
"We are all on the same page. As long as we are like this and we keep going forward, there will be no problems."
"Offensively, we have players in great form who are working hard, are making the efforts defensively for the team as well," Aurier said.
"For now, we are together, we work together, we win together and one day we will lose together but we will have to stay united. Like I said, I am not a dreamer but I would like to dream that at the end of the season we will be happy and be rewarded at last."