Despite being caught on camera entering the home of Barcelona president Joan Laporta on Monday morning, Jorge Messi denied said meeting but told reporters: "Of course, he [Messi] would love to return to Barcelona. I would like it too. We will see."
Barca expect to get approval from LaLiga this week regarding their financial plans in order to begin their transfer business, which will include the anticipated re-signing of Messi.
Asked if he had spoken to Laporta about how Barca could finance Messi's return, Jorge Messi said: "We spoke the other day, but there's nothing concrete."
Barca coach Xavi Hernandez said that Messi would make a decision regarding his future club this week and that "the doors are open" for his return.
Messi, 35, played his last game for PSG on Saturday.
The Argentina forward has contributed 21 goals and 20 assists for PSG in all competitions this season.
ESPN reported in April that Messi is considering a sizeable offer from Saudi Arabian side Al Hilal, although Jorge Messi denied later reports he had agreed to a deal.
Major League Soccer side Inter Miami CF are also interested in his signature.
Messi spent 21 years at Barca and helped the club win 35 trophies but left for PSG in August 2021 due to the club's financial crisis.