That's according to Italian football pundit Gianluca Di Marzio, who makes the revelation in his new book.
The fee would have been a world-record £225m transfer - Messi's buyout clause at the time - with Messi, Blues owner Roman Abramovich and then-manager Jose Mourinho keen for the deal to go through. He would have also earned £50m per season plus 70 per cent of image rights had the move not collapsed.
In his latest book 'Grand Hotel Calciomercato, a diary of the untold stories of the transfer market', Di Marzio details how contact between Messi and Chelsea first began in January 2014, reports the Daily Mail.
After speaking with several intermediaries as well as former Barca team-mate Deco, now an agent - who also had played at Chelsea, a meeting was set up with Messi and Mourinho via a FaceTime call.
That reported encounter went well with Messi telling his camp afterwards, "With Mourinho, for how he's spoken to me, I can win whatever I want: he's a winner, go ahead and close the deal".
Later that summer, Chelsea did business with Barcelona in the shape of signing Cesc Fabregas. And Di Marizo reports that it was a chat with Fabregas during one July pre-season session that saw the move break down between Messi and the Stamford Bridge outfit.
It is claimed that after his initial work to make the move work, Deco was squeezed out of talks as Mourinho spoke directly to Messi himself. Fabregas warned Deco of the situation and the former Portugal playmaker duly went to 'snitch' to Messi's father and agent Jorge.
Messi senior himself was angry at being excluded from negotiations with the personal terms already agreed by his son's intermediaries.
"I don't know what you're talking about, I swear," Messi reportedly told his father.
But it was too late and the potential mouthwatering deal was curtailed as he listened to his father and stayed at the Nou Camp.