Pogba, 26, has been linked with the Spanish giants and described Real as "a dream club for every player" while on international duty with France.
While Zidane, who recently returned for a second stint at Los Blancos broke silence on the rumours of a potential transfer by claiming he's a complete player that would be welcomed into his squad.
"He's a midfielder who knows how to defend and how to attack," Zidane said, as per BBC. "But he is not my player, he is at Manchester.
"He has always said that, after Manchester, Madrid has always interested him. So when his experience at Manchester ends, why not come here to Madrid?"
However, Solskjaer, who was recently appointed as the new permanent Red Devils boss, dismissed the notion of the club-record signing leaving any time soon.
"I don't like to talk about other teams' players, but that's the challenge with international breaks," he told reporters, as quoted by AS. "Players are available [to talk to the media] all the time and it's a different environment. It was a general talk.
"Paul is a very nice and polite man, who then answered a general question on it. To any kids in France, Zidane is an icon. He's a fantastic manager and was a fantastic player who I played against.
"Pogba's politely answered [a question]. He's happy here, he's going be a big, big part [of United's future]. I've always said you'd like to build your team around him, and that hasn't changed at all."