Chelsea have been disappointing in the Premier League so far this season and appear to be out of the running for the league title.
Meanwhile, Arsenal are currently second in the standings and are just two points behind leaders Manchester City.
“Chelsea prefer to defend when attacking is also an option,” Koeman told The Mirror. “Mourinho always chooses to defend.
“Even if his team goes 1-0 up, they would rather defend their lead than try to score more goals. Yet Arsenal can kill an opponent. That is why their victory against Manchester United was so impressive.
"Attacking-wise, they completely destroyed United. For 20 minutes, they played the most fantastic football, while Chelsea do the opposite thing.”
Koeman was referring to last weekend’s 3-0 victory for Arsenal against Manchester United at the Emirates Stadium in the Premier League.
The way the Gunners started the game was truly superb and stunned many, and they fully deserved the three points.
Mourinho has always been a manager who puts winning before everything else. The Portuguese’s teams do tend to play defensive football, but that has helped him win quite a number of trophies in his career.
The Chelsea boss in unlikely to change his style, and perhaps he should not.
The Blues are back in action next weekend when they take on Aston Villa at Stamford Bridge in the Premier League.