La Blaugrana have made an unbeaten start to the new league season but have conceded six goals and scored none in the Champions League so far, most recently suffering a humbling 3-0 defeat to Benfica earlier this week.
Koeman's future has been up in the air since the end of last season, although Barcelona lynchpin Frenkie de Jong does not believe that sacking the Dutchman is the answer.
However, the Daily Mail reports that Joan Laporta is set to sack Koeman no matter the outcome of Saturday's game, which the former Netherlands boss will not be on the touchline for due to suspension.
The report adds that Roberto Martinez is the Barca president's leading candidate for the role, but the club will only be allowed to spend £3.3m on hiring a new manager and coaching team.
Andrea Pirlo and Xavi have also been linked with the manager's job, but former boss Luis Enrique has ruled out the possibility of taking the reins again.
Koeman has won 37 of his 57 games in charge of Barcelona, and his side are currently sixth in the La Liga table after six games this term.
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