Messi recently left Paris Saint-Germain after two seasons in the French capital, becoming a free agent, with a return to Barcelona now his preferred option.
Jorge Messi told reporters: "Of course, he [Messi] would love to return to Barcelona. I would like it too. We will see."
The 35-year-old left the Catalan giants in the summer of 2021, signing for PSG on a two-year deal.
A move to the Ligue 1 champions happened after his former employers were unable to afford a deal under LaLiga's financial fair play rules.
During his time with Barca, he netted a record 672 goals in 778 matches, the club he joined as a 13-year-old.
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Now it looks as though an emotional return to the Spanish club is likely.
According to Gerard Romero, the club's financial feasibility plan has finally been approved by LaLiga.
Journalist Toni Juanmarti posted a video showing Messi's father at Laporta's house.
Cameras managed to corner him when leaving and reporters to began to ask him questions, where he spoke about his son's desire to return.
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Should his son re-sign for Barca, the club are understood to be prepared to hand him his famed No.10. jersey, make him the highest paid player at the club, and even give him the captain's armband.
A move back to Catalonia could potentially add €230million [£198.4m] in extra revenue every year, a much needed boost for the financially ailing club.
Messi has been linked with a move to the Middle East to Saudi Arabian side Al-Hilal, who are keen on the World Cup winner.
David Beckham-owned Inter Miami has also been touted as a potential destination for the footballing legend.