The 25-year-old, fresh off a two-goal performance in Barcelona's UEFA Champions League win over Spartak Moscow on Wednesday, still has four years to run on his current deal, but Barcelona club president Sandro Rosell is hoping the three-time Ballon d'Or winner will accept an improved deal so as to keep him at Camp Nou for the forseeable future.
Talks have not yet begun with the Argentina captain, but Rosell told Catalunya Radio he is hoping the deal can be done sooner rather than later.
"(Messi's current contract) finishes in 2016, but it would be irresponsible to not improve his contract," Rosell said. "You have to think about such things. Right now there is nothing scheduled, but this is a machine that is constantly in motion and things can change at any moment.
"The coaching staff think about next Sunday, we look further down the line and take the more distant future into consideration. Work has to start now on the contract that will take effect from 2016."
Rosell also spoke of his desire to keep captain Carles Puyol at the club, with the Spain international still having not signed a new deal despite his current contract only running until the end of this season.
"Puyol is an icon, a legend, he is our captain. We'd be delighted if he would end his career at Barca," he said.