The British prime minister is said to be considering a visit to lobby Crown Prince Mohammed bin Salman to increase the country’s oil output as energy sanctions on Russia begin to bite.
Government minister Michael Gove on Sunday did not deny a report in The Times on Saturday that Mr Johnson is to visit Riyadh this week.
He also defended Britain’s close ties with the Gulf nation after it executed a record 81 convicts in a single day on Saturday.
“We have to rely on oil from a number of countries, many of whose human rights records we don't approve of,” Mr Gove told Sky News.
“Saudi Arabia is a security partner of the United Kingdom. I think that there are human rights concerns. We're clear about those.
“But we also recognise that at a time when the world is in a fragile situation, that diplomacy alongside clarity on human rights is important.”
Britain and the US announced the end to Russian oil imports as part of sanctions against Moscow after its invasion of Ukraine.
Downing Street has not offered details of Mr Johnson’s travel plans for the week ahead.
He is scheduled to host a defence summit with leaders of northern European countries on Tuesday.
Fallout from the sanctions on Russia has sent prices of petrol and diesel in Britain to record highs, adding to a cost-of-living crisis as household heating bills also go up.
Mr Johnson last week said the UK and its allies were shifting away from dependence on Russian oil and gas, to avoid being further “blackmailed” by President Vladimir Putin.
Russia is the world's largest producer of gas and second-largest oil producer, behind Saudi Arabia.
The Times reported that Mr Johnson was well placed to lobby Prince Mohammed, having kept ties with him in recent years. Their relationship continued despite the killing in 2018 of dissident journalist Jamal Khashoggi.
The state-run Saudi Press Agency on Saturday announced the largest mass execution conducted by the kingdom in recent memory.
It said the group included people “convicted of various crimes, including the murdering of innocent men, women and children”.
Members of Al Qaeda, ISIS, and backers of Yemen’s Houthi rebels were also among the cohort.
“The accused were provided with the right to an attorney and were guaranteed their full rights under Saudi law during the judicial process, which found them guilty of committing multiple heinous crimes that left a large number of civilians and law enforcement officers dead,” SPA said.
“The kingdom will continue to take a strict and unwavering stance against terrorism and extremist ideologies that threaten the stability of the entire world.”
The kingdom’s last mass execution was in January 2016. It involved 47 people, including a prominent opposition Shiite cleric who had rallied demonstrations.