The Eredivisie giants will face 13-time winners Real over two legs in the last 16, beginning with Wednesday’s meeting at the Johan Cruyff Arena.
Ajax haven’t reached the quarter-finals of Europe’s top club competition since 2003, when they were beaten by eventual winners AC Milan, and won the last of their four European crowns in 1995.
And De Jong, who will leave Ajax at the end of the season to join Real’s great rivals Barcelona, believes there is everything to play for against a team that has won four of the last five Champions League titles.
"Our upcoming opponent is Real Madrid, a team that is starting to come in,” the midfielder told Het Kontakt. “I'm not going to say that we're going to win the cup. We'll see it from round to round.
“Real in the last five year, have won the Champions League four times, and they are favourites. But if we have a little luck, we are not hopeless.
“Apart from a few pains, I feel great fit. It makes a difference that we have a very good team and that every individual player also knows this.”
The Netherlands international agreed a €75 million (£65m/$85m) deal to join Barca in January, and will join up with his new club in July.
And he was questioned this week whether he will ask to take the number 21 shirt at Camp Nou, the same number worn for seven seasons by Barca legend and treble-winning coach Luis Enrique.
De Jong said: "In July I sign my official contract in Barcelona and I am also being presented to the fans and the press.
“Playing with 21 would be nice, because that is a bit my number. The selection for the new season is not yet known so I'll have to wait and see.
“Nike prefers that [I wear number 21] from a merchandising point of view, and I'm not sure if I want to.”