David Abel and his wife Sally are stuck on the Diamond Princess, which has been moored near Yokohama since 3 February.
The couple from Oxfordshire have been posting regular Facebook and YouTube updates from the ship.
In a Facebook update on Tuesday, Mr Abel posted: “There is going to be a time of quiet. We have been proved positive and leaving for hospital soon. Blessings all xxx”.
However, a short time later he expressed doubts that the couple have coronavirus, officially called Covid-19.
He wrote: “Frankly I think this is a setup! We are NOT being taken to a hospital but a hostel.
“That’s where partners are sent waiting out there [sic] quarantine.
“No phone, no wi-fi and no medical facilities. I really am smelling a very big rat here!”
When asked by a Facebook user about the test, he replied: “I doubt it was positive. If it was, we would be in hospital.”
When asked if the authorities were trying to keep him quiet, he replied: “Maybe”.
On Monday, the couple’s son Steve appealed to the British government to help his parents. He said the government’s response was “appalling”.
Speaking on BBC Breakfast on Tuesday, he said his parents are “very high-spirited people” but “there are cracks in the armour and they are getting down”.
He said: “My mum breaks down in tears frequently, my dad is short-tempered.
“They are not getting any communication from our country, so they are in the dark and feeling very unloved.”
When asked about the British government, he said: “They haven’t done anything.
“They aren’t communicating with us, the Foreign Office have my number, my wife’s number, my brother’s number, my sister’s number and they haven’t got back to us on anything and we have been calling them every day for four or five days.”