The Dutchman delivered the Copa del Rey trophy last term, but a largely disappointing campaign saw Barcelona finish third in La Liga and exit the Champions League in the round of 16.
The club's financial issues meant that they were unable to renew Lionel Messi's contract, which sent shockwaves around the world of football.
Koeman was strongly linked with a move away from Camp Nou at the end of last season, but according to Sport, the former centre-back now has the full backing of Barcelona.
The report claims that the club view the 58-year-old as the ideal manager to negotiate a difficult period, and the Dutchman could even stay in his position until the end of the 2022-23 campaign.
Barcelona have picked up seven points from their first three La Liga matches of the season, beating Real Sociedad and Getafe, in addition to sharing the points with Athletic Bilbao.