In his seven-and-a-half seasons with Spurs, the 29-year-old has suffered three defeats at the English national stadium - in the semi-finals of the FA Cup in 2010 and 2012 against Portsmouth and Chelsea, respectively, and to Manchester United in the 2009 League Cup final.
The only time Spurs have been successful at Wembley of late was five years ago when they beat Chelsea in the League Cup final - a game Dawson missed through injury.
Having regained his place in the Tottenham line-up after falling out of favour with manager Andre Villas-Boas, Dawson believes this could be the year he gets to lift a trophy.
"We spoke to the gaffer at the start of the season and we said we want to win trophies, as players and as a team," the Tottenham skipper told Spurs TV Online. "That's what you look back on at the end of your career. We have had two Wembley trips in the League Cup - one win and one loss.
"Wembley is a special place. To go up those steps and lift that cup would be special. And every player will say the same as me - the FA Cup is massive for us.
"We've had some good runs in it, we have been to Wembley twice, but had both unfortunate experiences against Portsmouth and Chelsea for different reasons. We want to go all the way and it would be a dream come true to do that."
Tottenham face Championship side Leeds in the fourth round on Sunday and Dawson believes his team will have to be at their best to avoid defeat at Elland Road.
"It's a one-off game. If we are not at the races we will come unstuck," said Dawson. "Leeds have some good players. It will be a sell-out, the fans will be right behind them and the atmosphere will be rocking so we have to be ready. (Leeds boss) Neil Warnock always gets his teams up for them so we have to be ready and we certainly will be."