Saudi Arabia's execution of Sheikh Nimr al-Nimr has angered Shi'ites across the Middle East and caused a major diplomatic row between revolutionary, mainly Shi'ite Iran and Saudi Arabia's conservative Sunni monarchy.
Saudi Arabia, Bahrain and Sudan broke all ties with Iran and the United Arab Emirates downgraded its relations on Monday after the Saudi embassy in Tehran was stormed by protesters. Kuwait recalled its ambassador to Iran today.
The Times reported Cameron had been due to visit Riyadh in the coming weeks as part of a tour of Gulf states, but that the trip would not go ahead until March at the earliest.
A spokeswoman for Cameron would not confirm that a trip to Saudi Arabia had been planned or delayed due to Nimr's execution.
Instead she said he was focused on his plan to renegotiate Britain's relationship with the European Union ahead of a membership referendum due by the end of next year.
"We don't confirm the prime minister's travel plans in advance. Securing reforms to the UK's relationship with the EU is a government priority and we would expect the prime minister to continue engaging with European leaders over the coming weeks," she said.
The British government has previously come under pressure over human rights issues in Saudi Arabia, considered one of its closest military allies in the Middle East. Cameron's spokeswoman said on Monday that Britain opposed the death penalty under any circumstances.