The Brazilian report, meanwhile – which comes from the same source that broke the news of Neymar's move to Paris Saint-Germain in 2017 – adds Messi has become more isolated at Barca than ever following the latest in a long line of embarrassing Champions League exits that extended his long wait for a fifth triumph.
Sunday night's claims follow reports Manchester City believe they would be in pole position to sign the Argentina star if he left the Nou Camp, something that would reunite him with Pep Guardiola.
However, City would likely face competition from across the globe, including from Inter Milan, whose former director Massimiliano Mirabelli has claimed Messi's signing "is more than a dream" for the club.
Messi cut a disconsolate figure last month after Barca surrendered their Spanish title to arch-rivals Real Madrid, with the Catalan club's captain criticising his team-mates and warning they would have to perform much better in what remained of the Champions League following the coronavirus crisis.
Messi inspired them to a last-16 second-leg victory over Napoli just over a week ago but was unable to prevent their capitulation to Bayern – which followed embarrassing exits at the hands of Liverpool and Roma in the previous two seasons.
Longer-term, Messi is said to have spent the past year battling Barca president Josep Bartomeu and the Nou Camp hierarchy over the direction of the club.
He was reportedly unhappy with the decision to sign Antoine Griezmann – who has been disappointing since joining last summer – instead of Neymar.