Messi's contract with Barcelona expires in the summer, meaning that he is able to agree a move to a foreign club should he decide his future lies away from Camp Nou.
Indeed, Messi had indicated to Barca that he wanted to leave only to be blocked from doing so, with the Argentine explaining that he would ultimately be staying until at least the summer of 2021.
But with no progress having been made over Messi extending his stay with the LaLiga club, there is speculation that he will look to end his time with Ronald Koeman's side and leave on a free transfer.
Manchester City and PSG are the two clubs that have been most heavily linked with signing Messi, with both among a select few that could afford the Argentine's wages.
And Messi's international team-mate Paredes has now expressed his hope that the Barcelona legend will join him in Paris, telling reporters: "It's natural that everyone wants Messi on their team, but it's the role of [sporting director] Leonardo and the president [Nasser Al-Khelaifi] to make the decision to convince him to join us.
"It's also a decision for Leo Messi. He'll choose the best for him but of course it would be great to have a player like him."
Despite speculation regarding Paredes' future and that he could be potentially moved on amid PSG's reported interest in Tottenham midfielder Dele Alli, the 26-year-old denied that he will be leaving.
He added: "I'll stay here. I'm very happy in Paris, with the club, with my team-mates and the coach. I'm very happy and I will be staying in Paris for several more years."
Paredes also discussed the arrival of Mauricio Pochettino, who has overseen three wins from his first four matches since replacing Thomas Tuchel, adding: "We take in and understand the ideas of the coach, we try to put them on the pitch, to do our best.
"The intensity of training has increased compared to what we did before."