The six-time Ballon d'Or winner is set to become a free agent next week as things stand, as he is yet to sign a new deal at the Camp Nou.
There have been reports that continue link the Argentine superstar with Paris Saint-Germain and Manchester City, while others claim a the club have offered the player a two-year deal.
Laporta has revealed that Aguero has been talking to Messi everyday about extending his contract with the pair currently on national duty at the Copa America.
"I would like Messi to tell us 'yes' as soon as possible. He would help us in every way," Laporta told Catalan media outlet La Vanguardia.
"Aguero is helping. He is telling him every day to stay.
"He (Messi) is excited and I am grateful to him for the desire he is showing to stay."