The mega deal would have been the biggest in football history if it'd come off - and would have smashed the £86m world transfer record that Real Madrid paid for Gareth Bale.
The reports from Spanish television station TV3 claim that Jose Mourinho tried his luck with a huge offer to lure the Argentinian star to the Premier League.
The formal approach, which equates to €150m, was rejected by the Catalan giants and Messi went on to sign a new deal in May to keep him at the Nou Camp until 2018.
Chelsea raked in around £80m in the last transfer window which would have given the Blues the financial clout to complete the deal.
Alex Harris of The Express has had more on the audacious prospect of Messi joining The Blues :
"Chelsea launched a stunning £118m (€150m) bid to buy Lionel Messi from Barcelona during the summer transfer window.
According to reports in Catalonia, the Blues submitted the cheeky bid for Messi due to his strained relations with the Barcelona board following last season's frustrating campaign which saw some of the club's fans criticise him for below-part performances.
Catalan channel TV3 aired a programme called Efectivament revealing that Jose Mourinho wanted to exploit Messi's then uncertain situation and persuaded owner Roman Abramovich to make an offer to the Catalan club.
However, neither Barcelona top brass or the 27-year-old were interested in the deal crushing Mourinho's faint hopes. "
It is being reported that Mourinho decided the time was right to try and persuade Messi to leave Barcelona after he suffered the most challenging season of his career.
The Argentine endured a string of injuries and was even the subject of abuse from some of his own fans for what they considered to be a below-par season.
Mourinho was able to sign Cesc Fabregas, Diego Costa and Filipe Luis in big-money deals over the summer.
Even without Messi, Chelsea have started well this term. They've dropped just two points in five games on their way to the top of the Premier League.
This isn't the first time Messi has been linked with a move away from Barcelona.
The 27-year-old was thought to have asked former Arsenal star Cesc Fabregas what life would have been like at The Emirates as the roof fell in on Barcelona last term.
On the back of a poor season and a delay in negotiations for a new contract Messi is thought to have cast his eye around some of Europe's top clubs as he plotted an escape route with his admiration for Arsene Wenger causing him to ask the question to Fabregas.
It's pretty hard to imagine Messi ever leaving Barcelona. He's played there his whole career, he's seemingly comfortable (and beloved) there, it's rare another club will be able to surround him with as much talent as he'll get at Barca and, oh yeah, it will take an enormous sum of money to pry him away.