Messi's fee would be a world-record one, and the contract is also worth £500,000-a-week, keeping him with the club until 2021, when he will be aged 34.
It is claimed Messi will be handed a "sweetener" of between £79m and £85m just to sign the new contract.
Messi is in the final season of his contract at Barca, and while his father and brother have signed off on a new three-and-a-half-year deal, the player is yet to do so as he is "reluctant to sit down with Barcelona's under-fire president Josep Bartomeu and give him what would be a "vote of confidence" opportunity".
Work on the "New Camp Nou" is not scheduled to start until 2019 but the stadium could be given a new name as early as 2018 with the company Van Wagner already studying the field of options.
Messi's current deal expires at the end of this season and, as things stand, he would be free to open talks with other clubs in January, but Barcelona are hopeful that the five-time Ballon d'Or victor will agree terms by the end of the year.
Messi is undecided as to whether November would be the right time to bring an end to speculation over his future.
One possibility is that he could potentially sign the contract with no photograph, therefore calming supporters' nerves, while also stopping the president from presenting the renewal as his personal success.
Meanwhile, the club's chief executive Oscar Grau has been criticised for saying Barcelona have the money to sign Philippe Coutinho in January. Liverpool must be rubbing their hands together'.