However, L'Equipe says Leonardo wants to bring the Spaniard to Paris in order to act as cover for their No1 next season.
For their part, Milan would be happy to grant Reina a free transfer in order to clear the €3m owed for the final year of his contract.
During the UK's coronavirus lockdown, Reina has stated: "After the loan spell with Aston Villa, I have to go back.
“I think it will be tough. I have 1-2 years left in my career. I think my time in football will end after next year in Milan.
“You never know in the future, but as a player I won't have a chance. As a coach, who knows."