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.
"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 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".
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 today that British ministers were at odds over an impending 5.9 million pounds (USD 9 million, 7.9 million euro) contract to provide a "training-needs analysis" for the Saudi penal system.
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.
"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.
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