The French giants had a massive 200m offer for the 16 year-old rejected by Barca in February.
Le Parisien says PSG refuses to give up hope on Yamal - who they would like to see replace the Real Madrid-bound Kylian Mbapp.
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PSG director Luis Campos has a very good relationship with the 16-year-old's agent, Jorge Mendes, and hopes that could open up a deal.
PSG have left their 200m offer on the table for Yamal and they could restructure it to make the proposal more attractive to Barca.
The superkid has scored six goals and eight assists in 44 competitive matches this season, including 24 starts.