Zidane has already lamented Madrid's forward options after Alvaro Morata moved to Premier League champions Chelsea.
French teenager Mbappe, 18, is reportedly at the top of Madrid's list after scoring 26 goals in all competitions last season.
Quizzed on his reported request for a forward following Madrid's 2-1 penalty shoot-out loss to Manchester United after Sunday's International Champions Cup clash finished 1-1, Zidane told reporters: "You know I will not ask for anything.
"I'm talking to the president. The staff. We have 28 here, and I'm happy with the job. Then we'll see what happens.
"Until August 31 anything can happen. I do not request anything."
On the match itself in Santa Clara, Madrid head coach Zidane was left pleased.
Marcelo, Gareth Bale, Toni Kroos, Luka Modric, Isco and Karim Benzema all played in the first half, which Madrid trailed to a Jesse Lingard goal.
Madrid's youngsters were given a chance to shine as Theo Hernandez, Oscar and Alvaro Tejero were introduced and helped force penalties via Casemiro's 69th-minute spot-kick.
Zidane, who said captain Sergio Ramos is close to resuming full training, added: "Very happy for this match. The kids played 45 minutes and they did very well. Satisfied, there were no injuries.
"We competed well. They played four games before. It is positive. Now we have another match. Hopefully we will find the shape little by little."