The Blancos defender has offered an invitation his international team-mate to join him at Santiago Bernabeu, where he has been for two and a half seasons
Since leaving Manchester United in the summer of 2012, Pogba has established himself as a regular for the Bianconeri alongside the likes of Andrea Pirlo, Arturo Vidal and Claudio Marchisio
However, transfer speculation has abounded of late that some of Europe's top sides - most notably Paris Saint-Germain - have been interested in making a bid for his services, and Varane says he'd delighted if Carlo Ancelotti signed his France team-mate."I have no information about any move," the 20-year-old told French football programme Telefoot.
"But personally, if it happens, I'd be very happy. I would love to play with him, but it's not my decision obviously."
Varane and Pogba are both regarded as two of the best young prospects in Europe and have established themselves in the France national team, making their debuts in the same game - a 3-1 win for les Bleus over Georgia last March in World Cup qualifying.