Chelsea value the player are closer to €30m (£27m/$34m), and as such will be forced to look elsewhere in their search for midfield reinrforcements with Zenit chief Alexey Miller likely to accept PSG's offer.
The Blues had hoped to bring the 24-year-old to Stamford Bridge as they try to replace the hole left in their squad following Cesc Fabregas' departure to Monaco.
Maurizio Sarri is keen to bring in a midfielder with a strong technical ability to act as a deputy to first choice Jorginho.
That player is unlikely to be Paredes, however, with PSG's hunt for a defensive midfielder of their own during the January transfer window set to come to an end.
They have been linked with Everton's Idrissa Gueye, Watford's Abdoulaye Doucoure and Borussia Dortmund's Julian Weigl during the course of the winter window as Thomas Tuchel looks to add to his own roster.
The Parisiens' need for a central midfielder has been intensified by an injury picked up by Marco Verratti against Guingamp on Saturday, with Adrien Rabiot also not in contention as he runs down his contract at Parc des Princes.
"We lost Adrien Rabiot, Lass Diarra and Marco Verratti, the situation has not improved.
"We stay with our decision [on Rabiot] because Marco returns in a few weeks. We stay with our basic choice.
"We have recovered Dani Alves in this role but it is very, very serious for us. Who do I want? Yeah, yeah, I know. Unfortunately I cannot tell you!"
PSG had previously held an interest in Chelsea's own N'Golo Kante, but following his decision to sign a new five-year deal with the Blues in November the French champions have decided taking that any further.