Ali Mohammed Baqir al-Nimr was 17 when he was arrested for taking part in anti-government protests in 2011.
Labour leader Jeremy Corbyn has urged Mr Cameron to directly intervene.
The PM said the government had raised the case but also defended the UK's relationship with Saudi Arabia saying it was important for national security.
"We have a relationship with Saudi Arabia, and if you want to know why, I will tell you why, " Mr Cameron told Channel 4 News on Tuesday.
"It's because we receive from them important intelligence and security information that keeps us safe.
"There was one occasion since I've been prime minister where a bomb that would have potentially blown up over Britain was stopped because of intelligence we got from Saudi Arabia.
"Of course it would be easier for me to say, 'I'm not having anything to do with these people, it's all terribly difficult et cetera et cetera.' For me, Britain's national security and our people's security comes first."
Mr al-Nimr was accused of taking part in anti-government protests in the eastern part of the country in 2011, involving the country's Shia Muslim minority, and was arrested the following year.
State media later reported he had been found guilty of a long list of crimes including sedition, breaking allegiance to the king, rioting, using petrol bombs against security patrols, robbing a pharmacy and more. He could be beheaded and his body displayed in public.
Last month, Mr Corbyn urged the prime minister to raise the case "directly" with his Saudi counterparts and "request that they commute the unjust and horrific sentence... which violates any number of international laws".
Mr Corbyn also raised questions about a Ministry of Justice bid to provide services to Saudi prisons.
Mr Cameron said: "We have raised this as a government. The foreign secretary has raised this, our embassy has raised this, we raise this in the proper way.
"I will look to see if there is an opportunity for me to raise it as well. We oppose the death penalty anywhere and everywhere and we make that clear in all of our international contacts."
David Cameron has said he will "look to see if there is an opportunity" to intervene personally on behalf of a protester on death row in Saudi Arabia.