The Spanish capital club are currently four points clear at the top of the Primera Division standings, but only last month they had a double digit advantage over their Catalan rivals.
Koeman believes that Madrid are feeling the pressure and that a defeat in Saturday's match will further complicate their quest for the Liga title.
"If Barca win on Saturday, it will be a heavy psychological blow for Madrid," Koeman told EFE. "Barca are more confident and Madrid are having doubts.
"Madrid will play for the draw. They will be conservative and will try to play at a low pace and hit Barca on the counter."
The two Liga giants lost their respective Champions League semi-final first legs in midweek, but Koeman believes that it will be an all-Spanish final.
"I am convinced that Barcelona and Madrid will be in the final," the Dutch coach said. "It will be a great match.
"Barca will turn the tie around, because they are better than Chelsea."
Starting last month and continuing for 10 weeks, Goal.com is publishing exclusive extracts from Luca Caioli's new book, Ronaldo: The Obsession for Perfection. The fifth extract, published on Friday, looks at the Portuguese's intense rivalry with Barcelona's Lionel Messi ahead of this weekend's Clasico clash. Don't miss it!