The meeting took place in a restaurant in Barcelona's city centre and lasted over two hours.
Koeman still has one year left on his contract at the Camp Nou, but ESPN reported earlier this week there are growing doubts among the board regarding his future at the club.
Despite the doubts, sources close to the club have told ESPN that Koeman could yet fulfill his contract due to lack of credible alternatives.
Sources close to the club also told ESPN earlier this week that Barca had contacted Bayern Munich coach Hansi Flick's representatives to sound out his availability this summer.
However, Barca were told that Flick, who announced in April that he would leave Bayern at the end of the season after leading the team to a Treble in 2020 and to the Bundesliga title this campaign, is expected to replace Joachim Low as Germany coach.
However, all three left the restaurant smiling and Laporta stressed that the meeting was routine, calling it "a normal meeting between a coach and a president."
Asked if the meeting had gone well, Koeman, who has been under pressure with some club directors feeling a fresh start is needed even if Barca were to win La Liga, said: "Very well. Good atmosphere."
Koeman did speak after Tuesday's draw and was asked if he feared for his job.
He said: "That's not one to answer now but after the last game of the season."
Koeman is no stranger to exit speculation as it has surrounded him since Barcelona's presidential elections on March 7.
Barca were reportedly eyeing Julian Nagelsmann, who is leaving RB Leipzig at the end of the season to take over for Flick in Munich, to replace Koeman after Laporta returned to the hot seat.
The former Barcelona star took the reins in August replacing sacked Barca coach Quique Setien shortly after the team's 8-2 defeat to Bayern Munich in the Champions League.
There had also been speculation that club legend Xavi Hernandez, who just signed a new contract with Qatari club Al Sadd, might be in line to become Barcelona coach, but sources say there is disagreement in the club about their former midfielder's readiness for the role.
Barca have won the Copa del Rey this season and are still alive in La Liga with two rounds remaining. However, Barca need slip-ups from La Liga leaders Atletico Madrid and Real Madrid to win the title.