The 46-year-old stepped down at the end of last season having masterminded a third successive Champions League triumph, but returned to the Bernabeu last month following the ill-fated reigns of Julen Lopetegui and his former teammate Santiago Solari.
Zidane was reportedly promised the opportunity to oversee an unprecedented summer overhaul following a disastrous campaign. To that end, Real have already agreed deals to sign Porto defender Eder Militao and Brazilian teenager Rodrygo but are far from finished with their summer business.
Eden Hazard is expected to arrive from Chelsea but Zidane, according to Marca, has his heart set on teaming up with his compatriot Pogba at the Bernabeu.
The former Juventus midfielder appeared destined to leave Old Trafford earlier this season following the total breakdown of his relationship with Jose Mourinho, but his form and demeanour have improved markedly since the appointment of Ole Gunnar Solskjaer.
Despite his and Uniteds upturn in fortunes, prior to Tuesdays Champions League demise against Barca, Pogba is said to remain intent on quitting Old Trafford for the second time in his career, but Real chiefs are unsure he represents value for money.