Cyril Abiteboul admitted the sponsored Dutchman "has some challenges" in using this year's Pirelli tyres.
Jul.27 (GMM) Caterham's team boss has refused to deny speculation Giedo van der Garde could lose his race seat.
Rumours in the past days and weeks have suggested the underperforming Dutch rookie could be replaced in the near future by former team driver Heikki Kovalainen.
When asked about the van der Garde/Kovalainen rumours in Hungary, team boss Cyril Abiteboul admitted the sponsored Dutchman "has some challenges" in using this year's Pirelli tyres.
"But just like everyone, he's being challenged, just like I am challenged on a daily basis by our shareholders.
"So like everyone, he has to deliver but he has no particular pressure, no more pressure than any other driver on the grid," Abiteboul added.
Meanwhile, van der Garde's teammate in 2013 is Charles Pic, who told RMC Sport that his future beyond this season is currently open.
"The key for me is to continue my development this year," he said.
"It's still too early in the season to talk about my future. I feel very good at Caterham, but if opportunities arise, we will look at them," added Pic.