Mauricio Pochettino's side claimed a huge victory against Manchester City on Sunday.
Spurs picked up an important 2-1 win away at Manchester City on Sunday to move within two points of current league leaders Leicester. But the Belgian has insisted that the side need to avoid talking about winning the title, and just concentrate on each game.
"We have to work hard and not dream too much, because if we dream too much, we can fall down very quickly," he told Sky Sports.
"We have to work hard like we did [against City] and see game by game. It is a very big win for us, but we don't talk about the title. Our goal is to reach the Champions League spots and I think we made a good step.
"There are still 12 games to play, so it is a long way. I am being 100 per cent honest - we don't talk about the title, because it is too far away."
While Mauricio Pochettino's men are still two points adrift of the table's summit, it is fair to say that they have much of the momentum. They have won their last seven games in all competitions, while the Foxes may have been left extremely deflated by Arsenal's late winner when the pair met hours before Spurs beat City.
As well as the run of form, it will also be the manner of the victory against Manuel Pellegrini's men that will please Pochettino.
Kelechi Iheanacho's equaliser appeared to give City a huge lift that suggested that if any team was going to clinch the win in the final 15 minutes, it would be the home side.
However, Christian Eriksen's late winner has severely dented the Citizens' title hopes, while also showing that this Tottenham side has the belief to beat anyone. And while Alderweireld would seemingly not like to admit it, that three points has confirmed that they are definitely genuine title contenders.