Pogba is expected to leave Juventus in the summer and has been heavily linked with Manchester United, Arsenal, Manchester City and Chelsea.
Menez's former club Paris Saint-Germain are also in the running to land the French international, but the winger believes that Real Madrid may be a better option.
He told beIN Sports: "Pogba to Real Madrid? It would not surprise me.
"He has what it takes to play there.
GETTY
Jeremy Menez says Paul Pogba could play for Real Madrid
He has what it takes to play there.
Jeremy Menez
"He is very respectful and has the respect of all the former players."
After previously admitting that Pogba is almost certain to leave, Juve chief Beppe Morata has since tried to play down talk of a move and has even suggested they may try to sign the player to an extension.
He said: "Juventus has not received any offers for Pogba and we have not sought any.
"We will not sell Paul.
"Pogba is one of the most skilled players in our squad and it is certainly not a priority of ours to put him on the market."
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