The Portuguese worldwide is expected to leave the Bernabeu this summer after Los Blancos decided not to offer him the new two-year contract he was looking for.
Speaking on Spanish radio station Cope Pepe said that one of the reasons to move on was because he was only offered a one-year contract.
However, Marca reports Emery instructed PSG to step up their efforts once Pepe's interest in the Nerazzurri became known. "One stage is over and, from now, another new one will start".
"It is clear that I will not continue at Real Madrid".
Pepe was previously said to be very close to signing for Italian side Inter, after agreeing terms.More news: Apple is bringing SteamVR and HTC Vive support to Macs
More news: Justin Bieber, other stars get emotional at One Love Manchester Benefit concert
More news: Putin gives new election-hacking theory during Megyn Kelly's NBC debut
Premier League clubs will be alerted by Pepe's comments after he added: 'There are more offers, also from England'.
The centre-back had been at the Bernabeu for ten seasons, winning the Champions League in 2014 and 2016 and he got a medal on Saturday despite not being in the squad.
Pepe was unhappy with the manner in which the negotiations took place and the "annoyed" defender explained why he decided against saying goodbye to Real's manager Zinedine Zidane.
"I do not want to blame anyone - what Zidane has done with Real Madrid is spectacular - but, there are things I do not understand".