The 26-year-old still has four more years remaining on his existing deal, but the Catalans are eager to offer their star player a new and improved contract which will make him the best paid player in the world.
Barcelona vice-president Javier Faus and general director Antoni Rossich met with Jorge Messi on Tuesday at the club's offices to present him with their contract offer and plans for the future and both parties will hold further talks on Wednesday to iron out a number of details.
The reigning Spanish champions are willing to pay Messi an annual salary of €20m after taxes, with the prolific attacker's new deal running until June 2019.
Sandro Rosell was forced to step down as club president following the controversial transfer of Neymar, while Fifa handed Barca a transfer ban, which has now been suspended following an appeal.
Nevertheless, the forward is excited about the project presented to him as the Blaugrana aim to rebuild their squad and has no intention of leaving any time soon.
Messi has netted 28 goals in 29 La Liga appearances so far this season and will be hopeful of adding to his tally in the next two games as Barcelona still have a shot at winning the Liga title.
They currently trail leaders Atletico Madrid by two points, but meet the Vicente Calderon side on the final day of the 2013-14 campaign.