They are said to be holding out for £133m but the report says Real are reluctant to pay such a hefty fee.
Their summer spend already stands at around £190m after the signings of Eden Hazard, Luka Jovic and Ferland Mendy.
Even so, Zidane is known to be a huge admirer of his fellow Frenchman and is desperate to sign him whatever the cost.
Pogba appears to be equally keen after claiming ‘now could be a good time for a new challenge.’
Paul Pogba is expected to leave Manchester United for Real Madrid (Image: GETTY)
"I am thinking of this: To have a new challenge somewhere else," he said.
"For me, I have been for three years in Manchester and have been doing great; some good moments and some bad moments, like everybody. Like everywhere else.
"After this season and everything that happened this season, with my season being my best season as well... I think for me it could be a good time to have a new challenge."
Pogba says he is looking for a new challenge (Image: GETTY)
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Zinedine Zidane is a big admirer of Pogba (Image: GETTY)
Gareth Bale is unsettled and Bayern Munich are said to be weighing up a loan deal.
Isco, Marco Asensio, Marcos Llorente and Dani Ceballos could all also be let go.
James Rodriguez is another player who is surplus to requirements and a good showing for Colombia in the Copa America could spark some interest.
He has been linked with both United and Arsenal and could yet return to Bayern after his two-year loan in Germany came to an end.