The bonus will be the highest ever and Barca are looking to sell the naming rights to the Nou Camp to help fund the deal.
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.
Catalan newspaper L'Ara (h/t MailOnline's Pete Jenson) reported Barcelona's wage bill already eats up 84 per cent of the club's overall revenue, a figure that does not account for the wages his new contract will entail or the signing bonus, which would be paid "across the years of his new deal".
The club could put the potential new sponsor's name to directors and supporters at the start of the new year.
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.
They may still organise friendlies for next month but there is an increased chance that Messi will have a potential window of opportunity to sign his new £500,000-per-week contract in the next global break.
Messi has been reluctant to sit down with Barcelona's under-fire president Josep Bartomeu and give him what would be a "vote of confidence" opportunity.
The Argentinian is undecided as to whether to sign the deal next month, with speculation over his future continuing to grow. He could opt to sign the new deal with no photograph.
Meanwhile, the club's chief executive Oscar Grau has been criticised for saying Barcelona have the money to sign Philippe Coutinho in January.