The La Liga giants are reportedly unable to pay Messi his current annual salary - believed to be around €75 million after taxes - in a new deal. With Barcelona facing debts totaling more than €1 billion, club president Joan Laporta is reportedly hoping to sweeten the deal by signing a star player like Erling Haaland or Neymar this summer.
Messi would rather renew his contract on a yearly basis, according to Marsden and Llorens.
Laporta said this week he's "convinced" Messi wants to remain at the club, vowing to do everything in his power to keep the 33-year-old from leaving at the end of his contract in June.
Messi has said he'll consider his future after the conclusion of the 2020-21 season. Barcelona can win the La Liga title if they win their final seven matches of the season.
Barca manager Ronald Koeman has been optimistic about Messi staying put.
"Leo has seen for quite some time that the team is improving thanks to all the changes we've made," Koeman said after Barcelona bowed out of the Champions League in March.
"Particularly, we have young players of great quality. We've got a great future ahead. Leo can't have any doubts about what the future holds for this team."
Barcelona have since won the Copa del Rey title - the club's first silverware since 2019.
Messi attempted to engineer his exit last summer, citing the lack of a project. But several academy graduates and youngsters have earned opportunities under Koeman, including Pedri and Oscar Mingueza, who scored in El Clasico in April.