The Catalan giants were held to a 3-3 draw by Levante in La Liga on Tuesday night, which has left them four points behind league leaders Atletico Madrid with just two games left.
Koeman's future is currently the subject of much speculation, with a recent report claiming that the La Liga outfit had identified Hansi Flick as a potential replacement this summer.
According to Marca, the Dutchman will meet with Barca president Laporta on Thursday to discuss the club's plans.
The report claims that Koeman's job is under severe pressure, but a final decision on the 58-year-old will not be made until after the team's final league match of the 2020-21 campaign against Eibar on May 23.
The former Southampton and Everton boss has won 33, drawn nine and lost 10 of his 52 matches in charge of Barca since arriving in August 2020 on a two-year contract.