Pogba has been the subject of transfer speculation in recent months after his agent, Mino Raiola, admitted he could leave Juventus in the summer.
Manchester United, Manchester City, Real Madrid and Chelsea have all been strongly linked with the Frenchman as a result.
Zidane believes it is only natural for the big clubs to be in for Pogba as he still has plenty of potential to improve.
When asked about Pogba’s future, Zidane said: “I don’t know where he’ll go and you’d need to ask him that because right now he’s with Juve.
“Considering his age and potential I certainly think he has plenty of room for improvement.
“When we are talking about a player like Pogba it’s only logical that Real Madrid and other big clubs are interested. It’s logical isn’t it? He’s young, strong and can only get better.”
Zidane’s comments may be interpreted as the start of a charm offensive by Madrid, as they have often worn players down before signing them when the transfer window opens.
Gareth Bale was the subject of a long-running saga at Tottenham Hotspur before he left for Spain last summer and the European champions look to be doing the same with United keeper David de Gea this term. Zidane himself has also got involved, phoning Raphael Varane to convince him to join Madrid rather than United when he left Lens in 2011.