Spanish news outlet Marca claim the Galacticos will recall Jesus Vallejo in the summer and let Pepe leave on a free transfer.
Vallejo, 19, has dazzled on loan at Eintracht Frankfurt and Real boss Zinedine Zidane views him as a future star.
“Real Madrid star Pepe has been linked with Man United and Chelsea”
The Mirror claimed earlier this season that Chelsea were monitoring Pepe’s situation closely as they look to bolster their defensive options.
A two-year-contract extension was mooted, but an agreement is yet to be reached.
And it now looks like the veteran star could be packing his bags in the summer.
Manchester United boss Jose Mourinho is also a long-term admirer of the Portuguese.
The former Chelsea boss isn’t averse to signing ageing stars and snapped up Zlatan Ibrahimovic in the summer.
Mourinho is trying to bolster his defensive options and he might be tempted to swoop for his compatriot.
The 33-year-old is currently able to hold talks with other teams and sign a pre-contract agreement from January 1.