Lyon, who managed a 1-1 draw at the Bernabeu on Wednesday to advance to the last eight 2-1 on aggregate, have never gone beyond the quarter-finals of European club football's showcase event.
But having eliminated Real in the knockout stage for the first time, they are now thinking they could go all the way to the final, to be played at the same venue on May 22.
NEWS:Lyon stun Real at Bernabeu
"I shouldn't say so but I did shed a little tear," Lyon president Jean-Michel Aulas, not a man to show emotions, told reporters after the match.
"Now we have crazy dreams in our heads, and one is to come back here for the final," he added.
After the sale of their two best players, France striker Karim Benzema and Brazilian midfielder Juninho, coming after Girondins Bordeaux broke their run of seven consecutive league titles in May, many supporters feared lean times were ahead.
Their concerns were realised in December, when Lyon found themselves trailing leaders Bordeaux by 13 points in Ligue 1.
However, a January training camp in Tunisia has proved a turning point in their season and Lyon are now just two points behind Bordeaux in the league after taking 20 points from a maximum 24 this year.
"We talked to each other a lot (in Tunisia) and a lot of things came into place after that", Brazilian defender Cris, the Lyon captain, told reporters.
The leading players have been setting an example since, with Argentine striker Lisandro Lopez scribbling a note with simple words urging the players to fight to the limit before Wednesday's match. The message proved an inspiration.
