The French manager is "desperate" to bring his compatriot to the Santiago Bernabeu, but club president Florentino Perez views him as overpriced, reports Rodrigo Faez and Alex Kirkland of ESPN.
The Spanish club has long been interested in signing Pogba; multiple bids were reportedly rejected this past summer. But Perez is unwilling to meet the Red Devils' valuation of the 26-year-old, which is well in excess of £120 million, according to Faez and Kirkland.
There's solidarity in the Real Madrid camp when it comes to Fabian Ruiz, though. The Napoli midfielder, 23, has already been identified as a summer target and is said to favor a move to the Spanish capital over Barcelona and Manchester City, who have also been linked with his services.
Ruiz, who has risen to stardom in Naples, is expected to garner a fee between £80 million and £100 million should he move.
Tottenham's Christian Eriksen and Ajax's Donny van de Beek have both been named as potential alternatives to the aforementioned duo, but Faez and Kirkland report that Zidane is not keen on either player.
Regardless of who arrives - if anyone - Madrid don't intend on making a splash until the summer transfer window, with Zidane wary of disrupting his side's cohesion midseason.