Messi is out of contract at the end of the season and the six-time Ballon d'Or winner has been heavily linked with PSG and Premier League giants Manchester City.
PSG sporting director Leonardo revealed the French powerhouse – now coached by Mauricio Pochettino – are pursuing Messi, after star and former Barca team-mate Neymar made no secret of his desire to reunite with the Argentina skipper.
Having talked up the possibility of Messi's arrival prior to PSG's 4-0 rout of Montpellier on Friday, countryman Paredes told Corriere dello Sport: "It's up to Leo to come to the club, because PSG are trying to convince him.
"To be able to be coached by a coach from your country and the possibility of playing with Leo is a great opportunity... I hope it happens."
Messi sat out Barcelona's 2-0 LaLiga victory at Elche on Sunday due to his two-game suspension following a red card in the Supercopa de Espana final defeat to Athletic Club.
The 33-year-old has scored 11 goals in 17 league appearances for Barca this season, while he has 14 across all competitions.
PSG, meanwhile, are top of Ligue 1 on goal difference ahead of Lille through 21 rounds.