The Argentina international's current contract at Camp Nou is due to expire at the end of June, and there has still not been an announcement over a potential extension.
Laporta has insisted that discussions with Messi "are going well", and he is "optimistic" that an agreement will be found with the 33-year-old, who continues to be linked with Manchester City and Paris Saint-Germain.
"I would like to say that [Messi's contract renewal] is already done, but it is not like that," Laporta told reporters. "The talks are going well, but it is not done. The idea is to reach an agreement as soon as possible. It is convenient for him and also for us because if we solve this matter others would be solved faster.
"We are confident because he wants to stay. We are doing everything possible to offer him a competitive team. We have signed Kun [Sergio Aguero] who reminds him every day at the Copa America that he has to sign so they can play together.
"I am not contemplating [getting] a no [as an answer]. I am optimistic. He wants to stay and we do what we can. It is not easy. He is still the best in the world and is coveted by other clubs that have greater financial potential.
"We compete against state clubs that can undermine transfers that we are trying [to carry out]. It is not fair. We live in a difficult moment in which it is not enough to make an offer and reach an agreement. Now things have to fit together. And this requires patience."
Messi enjoyed another impressive season at Barcelona despite the speculation surrounding his future, scoring 38 times and registering 14 assists in 47 appearances in all competitions.
However, the Catalan giants endured an underwhelming campaign despite winning the Copa del Rey, having finished third in La Liga and exited the Champions League in the round of 16. body check tags ::