Northern Ireland sit third in their group, three points behind both Germany and Slovakia with two games remaining.
They face Slovakia in Kosice on Friday before ending their campaign at home to Luxembourg three days later. The group winners qualify automatically for next summer's tournament and the runners-up going into March play-offs.
"It would be special to get to a major tournament with my country, it's something I dream of," said Bradley.
"We know how tough it is, and it hasn't happened much in the past, but I've full belief in this group of players.
"We've a really good team and really good young players. Hopefully we can get there."
On his form, Bradley also said: "Whenever you play for a club like Liverpool, there's pressure and there's eyes on you all the time. I've started to realise that over the last two years.
"You've just got to try and be as consistent as you can every time you go out there and play. It's just very hard work every day and making sure you're at it and making sure you look after yourself, because the Premier League is relentless.
"Obviously, last season was really disappointing. I don't think it was anything individually on me, but it was more just unlucky with (injuries). You've just got to look after yourself in the best way possible."