This claim is made by The Daily Express, who suggest that the La Liga runners-up appear to be stalling over a new contract - which could lead to heavyweight Premier League interest in the world's greatest footballer.
Indeed, the same source points to a rather intriguing selection of recent comments from Messi, in which he appears to re-iterate his desire to remain at Barcelona but states that he may have to look at another solution if he does not feel the same affection from the club.
For many, the possibility of four-time Ballon d'Or winner Messi leaving Barcelona is simply unthinkable as the Argentine maestro has become synonymous with the Catalan giants for the entirety of a truly illustrious playing career.
As the unrivalled jewell in the club's crown, Messi has won six league titles to date at the Camp Nou, as well as two Copa del Reys, six Supercopa de España titles and three Champions League crowns.
If reputable Premier League clubs such as Manchester United and Chelsea were indeed to even attempt to buy Messi, you have to assume that they would have to pay a truly extravagant fee to make the deal happen - the kind of money only reserved for the very best.
Manchester United's recent financial performance would suggest that they could well have a lot of money to spend in the coming years, while Chelsea certainly
Champions Manchester City could provide an alternative of course, although the Citizens have been recently hit with a hefty fine from UEFA for breaching rules relating to Financial Fair Play (FFP).
If Messi were indeed to ever come on the transfer market, as alien a concept as that might be for so many passionate Barcelona supporters, it would also be particularly interesting to see if Pep Guardiola - his former manager - would be able to engineer a potential reunion in Germany with his dominant and formidable Bayern Munich side.