Mbappe, 18, remains the most sought after young player in Europe after his stunning breakout campaign with Monaco last term with Arsene Wenger one of his many admirers. The Gunners boss has already tried to sign him on one occasion but Real's interest in the France international threatens to scupper their interest.
Monaco recently threatened to take legal action against any club that makes an illegal approach for their prized asset, following a number of reports of meetings between the player and officials from Manchester City and Paris Saint-Germain.
Real's interest remains, however, heightened by Alvaro Morata's recent move to Chelsea. Speaking ahead of his side's pre-season friendly against Manchester United on Sunday, Zidane was asked if his squad was now weaker following the Spaniard's departure, replying: "It certainly is. We saw what he did last season. He gave a lot to the team. Right now we are missing a striker," AS report.
While Zidane is concentrating on working with the group of players he has at his disposal at the moment, he is hopeful of making further additions following the arrivals of Theo Hernandez and Dani Ceballos, aged 19 and 20 respectively.
Inevitably, Mbappe's name was mentioned when discussing those possible further additions, but the Real boss was giving little away.
"There are 28 with us at the moment and they are what I am focused on. As always until the 31 August anything can happen. He [Mbappe] is good but I am only thinking about tomorrow's game and preparing for the season ahead."
He added: "It is true that some very good players have left and some young players have come in, but we are trying to improve the overall squad. We are pleased with those lads that have arrived recently, they are passionate to be with us. They know where they are but the season will tell us if we have improved the squad."
According to latest reports from Marca, however, Monaco will demand £170m from any club looking to sign Mbappe the summer, a figure they hope will act as a deterrent rather than a realistic selling figure.
Monaco vice-president Vadim Vasilyev is well aware of the potential transfer of Neymar from Barcelona to Paris Saint-Germain for a staggering £199m and will use that move as a precedent should any club wish to sign his player this summer.