Carlo Ancelotti's men currently top the Primera Division standings by a point ahead of rivals Barcelona, who they will face in the Copa del Rey final next month.
The capital club are also pretty much assured of their spot in the quarter-finals of the Champions League after defeating German side Schalke 6-1 in the first leg of their last-16 clash.
With several players hitting peak form since the turn of the year, Zidane is optimistic Real can win all three tournaments for the first time in their history.
"Of course you should discuss the possibility of winning the treble," he said in an interview with Spanish newspaper El Confidencial.
"When you play at Real Madrid you know what the objectives are. We are in three competitions and we are there.
"We must go on, knowing that it is very difficult because there are very good teams. If you remain focused and working well, we can achieve important things."
Real are unbeaten since suffering a 2-1 defeat at Barcelona on October 26 - a run of 28 games in all competitions.
"It's an awful lot of games," Zidane added. "You know what's the secret? The players. We also have a very good coach who leads the group."