The deal, if completed, would easily surpass the £83 million Real Madrid paid for Gareth Bale last summer, and would also make Messi the best paid player on the planet.
Although there have been murmurings about Messi's future at Barcelona for some time, the fact he put pen to paper on a bumper new contract last month seemed to have put the speculation to bed.
However Le10 Sport claim that PSG are retain hope of pulling off the biggest transfer in football history, and have agreed to hold further talks after the World Cup is over. Messi is currently away with the Argentina squad in Brazil, and should he help his side reach the final then talks won't take place until after July 13.
The only way PSG will be able to prise Messi away from Barcelona is by meeting the release clause in his contract, which stands at an eye-watering €250 million. The decision to resume talks after the World Cup concludes came about after a six hour meeting between PSG and representatives of Messi as well as the Barcelona star himself.
Talk of a record-shattering transfer being concluded between the end of the World Cup and the end of the summer transfer window in August seems fanciful at best. A deal of that magnitude, and one that Barcelona would likely do all they could to fight would take months to conclude, even with the presence of a release clause.
Then there is the restrictions placed on PSG by UEFA, who are trying to stop reckless spending through their Financial Fair Play directive.
According to European football's governing body, the Ligue 1 champions had agreed to "significantly limit spending in the transfer market for seasons 2014-15 and 2015-16", while they have also committed to recording losses not in excess of €30 million for 2014/15.
That would seemingly make spending €250 million on one player seem impossible, plus the cost of his wages, likely to be a significant increase on the £15 million he currently takes home each year, will further add to that cost.
Messi's future at Barcelona doesn't quite seem as certain as it once did. Although he has penned a new deal with the club, their failings on the field and his spat with club directors off it - along with a high-profile tax case - have tarnished his reputation somewhat.
That's not to suggest he could move this summer or even next, but with Barcelona in a state of flux after a disastrous campaign last time round, Messi may well be considering his options.
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