Ex-Bayern Munich player Dante has helped Nice climb to the summit at the midway point of the season.
They are two points clear of nearest rivals Monaco and five ahead of champions Paris St-Germain.
"Anything can happen. We need to concentrate 100%. We have a chance," said Dante in an interview with BBC World Service's World Football.
Lucien Favre's side have lost just one of their first 19 league games and entertain struggling Metz on Sunday.
"When I wake up I only think to win every game because this season we can make some big dreams come true," added Dante, who joined Nice from Wolfsburg in August.
Former Manchester City striker Mario Balotelli has scored eight goals in nine league games for Nice since joining from Liverpool in August.
Dante said: "Mario is world class. He is so important here and a very good guy.
"Everybody says he is bad boy. Maybe in the last group he made some mistakes but I speak to him and he only wants to play football now."
Listen to World Football's full interview with Dante.
Nice can "make dreams come true" by winning Ligue 1 for the first time since 1959, defender Dante says.