The club have made a solid start to their 2021-22 La Liga season, picking up seven points from three matches to occupy seventh, but they suffered a 3-0 home defeat to Bayern Munich in the Champions League on Tuesday.
A disappointing 2020-21 campaign, which saw Barcelona finish third in La Liga, piled the pressure on Koeman, but the Dutchman managed to keep his job at the club over the summer.
According to Sport, the 58-year-old's position at Camp Nou would be in severe doubt if the team slip up in any of their next three fixtures against Granada, Cadiz or Levante.
The report claims that Barcelona president Joan Laporta is already putting plans in place in the event that Koeman is relieved of his duties.
The former Southampton and Everton manager has taken charge of 58 matches for the Catalan giants and boasts a record of 36 wins, 10 draws and 12 defeats. body check tags ::