It's sport and everything is possible - Tuchel
The Blues were beaten 3-1 by the Spanish side in the first leg of their quarter-final and travel to the Bernabeu for the return leg on Tuesday.
Chelsea won the competition last season under Tuchel.
"It is one of the biggest challenges to perform away at the Bernabeu," said the German.
"It is even more difficult if you have to earn a certain result, if you need to win with a minimum of two goals or better or maybe a three-goal difference. That makes it almost impossible and very, very difficult, but still it is worth trying.
"We need nothing else than a fantastic script that we want to be able to overcome this."
Chelsea knocked Real out of the Champions League at the semi-final stage last season after a 1-1 draw in Spain - in a game played at the Alfredo Di Stefano Stadium - before following that draw up with a fine 2-0 win at Stamford Bridge.
Real have won Europe's top competition a record 13 times and no English side has ever won a Champions League game at the Bernabeu by more than a single goal.
"The task is incredibly high and the challenge is incredibly high given the circumstances of the first leg, where we play, against whom we play and at what stage we play this kind of match," added Tuchel.
"It is sometimes important to imagine things and to dream about it, but it will not shift the focus from the fact that we need to deliver and we need to be ready.
"We will arrive and try everything because it's worth trying. From there we see and, hopefully, we have a match where belief grows within the match by our actions and, hopefully, we can fulfil our dream, live up to our dream.
"But realistically, we have to invest a lot and be at our very top level."
Real Madrid manager Carlo Ancelotti is bidding to qualify for the Champions League semi-finals for the eighth time in his career, which would be the joint most by a coach in the competition along with Pep Guardiola and Jose Mourinho.
"Chelsea will come here to rescue the tie, I have no doubt about it," said Ancelotti.
"He [Tuchel] can say whatever he wants but I'm sure Chelsea will come here to win - that's the spirit of football, the spirit of big clubs and great players, to never give up.
"I'm lucky to have a group of players that know these types of games really well, that anything can happen. They are in a good spirit and happy with the opportunity to reach a Champions League semi-final.
"But Chelsea are a very strong rival. We have to have a lot of respect and we're going to have it".
-- Courtesy of BBC Sport