The belief of the Rangers is getting stronger after they defeated Red Star Belgrade in the last 16.
The Serbian side were eliminated 4-2 on aggregate by the Scottish champion.
Rangers have made the quarter-finals of a European competition for the first time in six years, but fans will be daring to dream.
Van Bronckhorst said he was proud and happy for everyone involved with the club.
Concerns have been raised about the domestic form of the reigning champion.
Rangers went from having a four-point lead over Celtic to trying to get back in the game. The European exploits of their successor cannot be discredited.
The first game in charge was against Sparta Prague. A two-goal victory was required to book a knockout place.
Rangers were runners-up in the group after a good draw at Lyon in the final game.
The general consensus was that the European adventure would come to an end against the German giants when they were pulled out of the hat.
The Govan side were drawn with Serbian champion Red Star in the last 16 after a famous 6-4 aggregate victory.
The first-leg win put Rangers firmly in the driving seat, and despite a loss in the second leg in Serbia, the Ibrox club advanced to the quarter-finals for the first time in 14 years.
Rangers have been inspired by goalkeeping by 40-year-old Allan McGregor.
The oldest keeper to make at least 11 saves in a game is the ex-Scotland keeper, who made vital saves at defining moments in the tie to prevent Red Star making it a more nervy evening for Rangers.
The last time Rangers reached this stage of European competition, in their run to the 2008 Uefa Cup final, McGregor was on top form as Rangers battled to a last-16 victory at Werder Bremen - a sign, perhaps, that history may repeat itself.
At times he needs to be there, according to Van Bronckhorst. He is important for us even at his age.
The opponent will be stronger as Van Bronckhorst evades to post- match.
If you skim through the potential last-eight opponents of Rangers, you will wonder if you are looking at the European Championship instead.
The glamour ties would include a reunion with Lyon and West Ham United.
On paper, the likes of Portugal's Braga, who Rangers dumped out in the last 32 of the competition, and Eintracht Frankfurt, who sit ninth in the German top flight, look good.
The men will embrace any challenge, even if they are competition favorites.
The ex-Scotland international said she didn't think Rangers would fear anyone. If you want to win the thing, you have to knock out the big guns.
Mark Hateley said that Barcelona aren't what they were.
Richard Foster is a former Rangers right-back.
The teams left in the competition are going to make it difficult. You can't rule them out because they have come past a decent Red Star team.
To be in the semi-finals of the Scottish Cup and still be battling Celtic for the league, Van Bronckhorst has to use his squad.
The ex-Scotland international is on Sportsound.
There are going to be huge questions asked of the squad over the next few weeks, so you will see how good they are.
The scheduling is going to intensify. The Old Firm and the quarter-finals of this tournament are now semi-finals.
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