The Spanish outfit were beaten 3-0 in their Champions League opener on Tuesday and several members of the club’s board had a meeting to demand his exit.
Laporta is thought to be under pressure to dismiss Koeman as the manager of Barcelona.
It will be interesting to see if the Barcelona chief decides to let go of the Dutch manager and bring in a replacement in the coming weeks.
Koeman has a contract with Barcelona until the summer of 2022 and the Spanish outfit would have to pay him a severance package if they decide to sack him now.
Barcelona are already under financial pressure because of their rising debt and they might not want to pay a severance package right now.
The Barcelona manager has some winnable fixtures coming his way and he could still salvage his future at Camp Nou if he manages to win them.
The Catalan giants will be facing the likes of Granada, Cadiz, Levante and Benfica in the coming weeks.
Koeman has won just one trophy with the Spanish club since taking over. Barcelona won the Copa Del Rey under his management last season and the fans will be expecting him to guide the club to a league title this year.
The likes of Real Madrid and Atletico Madrid have stronger squads at their disposal and winning the league will be a massive challenge for Koeman.