Messi and club captain Andres Iniesta are entering the final 18 months of their current deals at the Camp Nou meaning they would be free to talk to other clubs in a year's time if they don't extend their contracts in 2017.
Despite posting a record turnover of 679 million euros ($719 million) last season, a series of expensive new contracts for the likes of Neymar and Luis Suarez mean Barcelona are close to overstepping the 70 percent limit of turnover spent on salaries imposed by UEFA's financial fair-play laws.
"We have to be very strict with the budgets, we can't go crazy," said Barcelona CEO Oscar Grau, confirming that the Catalan giants have no plans to strengthen the squad in the January transfer window.
"We need to comply with the ratios of debt and the percentage of salaries in the budget."
Five-time World Player of the Year Messi, 29, and Iniesta, 32, have been at the club since they were teenagers and have been the cornerstones of the most glorious period in Barcelona's history, each winning eight Spanish league titles and four Champions Leagues.
"We want the best player in history to remain here at Barcelona and we want to renew the players that have been brought through here. They are the best and they should retire at home," added Grau.
"We have to analyse it. We are working with common sense and discretion. We want Messi to stay and we will find the way, I am sure. I want to calm all Barcelona members."
Any new deal for Messi is likely to see him usurp Cristiano Ronaldo, who recently extended his Real Madrid deal to 2021.
The pressure on Barca's salaries is set to be eased when bumper new shirt-sponsorship deals with Japanese retailer Rakuten and kit manufacturer Nike worth an estimated 210 million euros a year kick in from next season and 2018 respectively.
Meanwhile, the start date for a major redevelopment of the Camp Nou has been delayed from later this year to July 2018.