Koeman met with Laporta, who was elected in March, during the international break to discuss Messi's future and possible summer signings. Laporta later met with Borussia Dortmund striker Erling Haaland's agent, Mino Raiola, and the player's father, too.
Messi, 33, is out of contract in June and has not yet decided on his next move. He wanted to leave Barca last year under the previous regime but there is renewed hope he will stay following improved performances on the pitch and the return of Laporta, who was previously the president at Camp Nou between 2003 and 2010.
"It is a really important issue and we will do everything we can for Leo to spend many more years at this club," Koeman said in a news conference on Sunday when asked if the club would set Messi a deadline.
"But, at the moment, it's not about next season, it's about [Monday's] game against Real Valladolid. The president and his people can deal with the future.
"As I said a couple of weeks ago, we took advantage of the international break to have a meeting with the president and the board to speak about this season and next season. It happens at all clubs in the world, but the players and I are focused on our upcoming games."
Sources have told ESPN that Laporta wants to wait for the results of an internal audit before offering Messi a new deal. However, he has repeatedly expressed his desire for the Argentina international to remain at the club, including in his inauguration speech last month.
Meanwhile, Koeman and Laporta will try and convince Messi to stay by building a team capable of challenging for the Champions League, a competition Barca have not won since 2015, in the coming seasons.
Koeman wants to add a striker to the squad and sources have told ESPN that Haaland is the "dream" signing. However, with the club's gross debt standing at €1.2 billion and the wage bill needing to be trimmed, there are doubts about whether a deal for the Norway forward is possible.
Laporta met with Raiola and Haaland's father, Alf-Inge, on Thursday to discuss terms -- Haaland has a €75 million release clause which kicks in next year but would cost a lot more this summer.
Raiola and Haaland Sr. have also met with Real Madrid representatives, while there's also interest from several Premier League clubs, although City coach Pep Guardiola suggested it would be impossible for his side to spend big in the financial climate with the coronavirus pandemic causing losses across football.
"I don't know if it's possible because we spoke about the future of this team and the final decision is always by the president of the board if something is possible or not," Koeman said when asked if Barca could afford Haaland.
"It's not for me to give an answer to this question because I am not involved in the financial situation of the club. We spoke about how we can improve the team and the final decision is always with the president."
Following the international break, Barca return to league action against Valladolid at Camp Nou on Monday. Valladolid could be without up to 12 players due to injuries, suspensions and a coronavirus outbreak at the club.