The Argentine is out of contract at the end of the season and is yet to put pen to paper on an extension.
Last month, Barcelona president Josep Bartomeu insisted the only thing missing was his signature after agreeing a new £500,000-a-week deal.
And Catalan paper L’Ara report Barca will hand Messi a bonus between £79m and £85m when he agrees his contract.
With Messi having fired Argentina to World Cup glory this week, he has opened the window to sign his contract during the next break in November.
Barca could pay for the deal with help from a new Nike deal and a stadium sponsor for the Nou Camp.
They are preparing for a £500m renovation of the iconic venue, where the capacity will be increased to an incredible 105,000 by the end of the 2021/22 season.
Sport reports that Barca have already began negotiations with global companies over the possibility of taking the rights.
The Catalan giants are hoping for in excess of £179m in a deal.
Meanwhile, Sergio Aguero has said he would Messi to join him at Man City but acknowledged that it would be difficult for his compatriot to leave Barcelona.