Philip Hammond will raise the case of a 74-year-old British expatriate grandfather threatened with flogging for breaking Saudi Arabia's strict anti-alcohol laws during his visit to the Gulf state.
The Foreign Secretary has held talks with the country's ruler King Salman and will hold a series of meetings with other members of the royal family and officials during his visit.
Among the issues on the agenda is the case of Karl Andree, who has served his time in jail but is still locked up as Saudi officials wait to carry out the lashings, according to his family.
David Cameron has already intervened in the case and Mr Hammond will use his talks to try to make further progress, a Foreign Office source said.
A Foreign Office spokesman said: "As usual on all visits, he will raise consular cases, including current Saudi judicial cases."
The visit, which senior Government officials stressed had been in the diary "for quite some time", comes just days after Saudi Arabia's ambassador to the UK warned of an "alarming change" in the relationship between the two countries.
Mr Hammond said his four-nation tour of the Gulf would allow him to talk to "key partners" about "security issues" ahead of a major conference on Saturday.
The visit follows the ambassador's warning of "potentially serious repercussions" of a breakdown in relations with the UK and a lack of "mutual respect".
Prince Mohammed bin Nawaf bin Abdulaziz singled out the cancellation of a deal to train prison staff in the Gulf state as he railed against an "alarming change in the way Saudi Arabia is discussed in Britain".
In an unusual public intervention, he wrote an article for the Daily Telegraph in which he warned the wealthy kingdom would not be "lectured to" and urged respect for its strict system of Sharia law.
As well as Mr Andree's case, the links between London and Riyadh have been strained by the cancellation of a bid for a Saudi prison consultancy contract.
As part of the tour, Mr Hammond will meet the leaders of Saudi Arabia, Qatar and the United Arab Emirates to discuss regional security and the crisis in Syria, ahead of international talks in Vienna on Friday.
At the weekend, he will give a speech on extremism - which he described as "the great challenge of our time" - at a summit in Bahrain hosted by the International Institute for Strategic Studies.
The Foreign Office said he will make clear that the UK's national security is heavily linked to that of the region, highlighting continued commitment to a military presence in the Gulf.
Human rights groups said Mr Hammond should use the visit to press for action on a range of cases, including Ali al-Nimr, who faces crucifixion and beheading, and the blogger Raif Badawi who was sentenced to 1,000 lashes and a lengthy jail term.
Amnesty International UK spokeswoman Lucy Wake said: "Despite the Saudi Arabian ambassador to the UK's recent threats to the UK, the Foreign Secretary should refuse to wear a Saudi muzzle.
"Mr Hammond musn't be cowed - he should stick to a principled position of raising urgent cases like that of the young death row inmate Ali al-Nimr and the jailed blogger Raif Badawi.
"There's a catastrophic civilian death toll in Yemen, with even hospitals being bombed, and we fear UK weaponry is being used by reckless Saudi forces.
"Mr Hammond must inform the Saudi government that the UK is not willing to be a party to terrible war crimes in Yemen, and is suspending arms exports to Saudi Arabia while that risk remains."
Reprieve's Kate Higham said: "Despite the Foreign Secretary's hint last week that he 'does not expect' the Saudis to carry out hideous punishments on Ali al-Nimr and Karl Andree, it appears these assurances are shaky at best.
"There are still grave fears for Ali and the other Saudi juveniles facing execution – while Ali's father was also yesterday detained after speaking out to save his son's life. The UK is one of Saudi Arabia's closest allies – Philip Hammond must use his visit to demand an end to these terrible abuses."