Karl Andree has served a year in jail but has been told he could face a public flogging.
His family say they fear the punishment could kill him and have urged the British government to intervene.
Read: Selection of Saudia Arabia to head UN human rights panel sparks anger
"He's done his time now; he should be released. This lashing sentence - we fear, because of his age, he won't survive it," his son, Simon, told BBC radio.
"He's a frail old man... enough is enough."
The Foreign Office said it was actively seeking his release.
The Sun newspaper said that despite having served his sentence, Andree was still in jail as Saudi officials wait to carry out the flogging.
Saudi Arabia's legal code is based on Islamic sharia law.
The cancer-surviving grandfather of seven has lived in Saudi Arabia for 25 years, working in the oil industry.
His wife Verity has returned to Britain for full-time care due to her worsening Alzheimer's disease.
Andree's son implored British Prime Minister David Cameron to intervene personally, but feared that his father was "at the bottom of the list".
"I feel that all the business dealings with Saudi Arabia and the UK are probably taking priority," he said.
Saudi Arabia is Britain's most important trade partner in the Middle East and was its biggest market for arms exports last year.
The Times newspaper reported Tuesday that British ministers were at odds over an impending £5.9 million ($9 million, 7.9 million euro) contract to provide a "training-needs analysis" for the Saudi penal system.
Read: Germany slams Saudi Arabia's offer to build mosques for Syrian refugees as ‘cynical’
It said Justice Secretary Michael Gove wanted to pull out of the deal agreed by his predecessor, but Foreign Secretary Philip Hammond thought it would make Britain look untrustworthy to a key ally.
A Foreign Office spokesman said: "Our embassy staff are continuing to assist Mr Andree, including regular visits to check on his welfare, and frequent contact with his lawyer and family.
"Ministers and senior officials have raised Mr Andree's case with the Saudi government and we are actively seeking his release as soon as possible."
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ