 Videos of Mr Bigley have been broadcast on Arabic television |
The brother of Ken Bigley says he has heard the hostage has been handed over to a group who are preparing to make a ransom demand. Paul Bigley made the claims, which he says are "unofficial", while speaking to BBC radio Hereford and Worcester.
He said the process of freeing his brother would be made "a little easier" if the reports are accurate.
The Foreign Office said the rumour is understood to have first appeared in a Kuwaiti newspaper over the weekend.
A spokesman said the reports are currently being investigated.
Speaking on BBC News 24, Paul Bigley said the unconfirmed reports had given him some hope.
The hostage's brother said: "If the whole scenario has switched from a political scenario to a financial one it makes it a little easier."
"If it takes pennies or dollars to get Ken free, then yes of course," he added, when asked if he would consider taking part in a ransom deal.
He said: "I don't agree with it, and I would have to count to three and swallow."
'Gut feeling'
Mr Bigley, a 62 year-old engineer from Liverpool, was taken hostage on 16 September by the hardline Tawhid and Jihad group, along with two American colleagues who were beheaded a few days later.
Media reports in Kuwait claimed the fundamentalist group were considering selling the hostage to another militant group who would then demand a cash ransom.
The new group, who are more moderate, are said to be the same organisation that released two Italian women last week.
Paul Bigley believes the transfer has already taken place.
He said: "It is my gut feeling, and the gut feeling of about 25 prominent people in Kuwait, that Ken is being held by a new group.
Multi-faith walk
"The people telling me this are decent, honourable and high-level people, so I trust their instincts. Whether it will be confirmed remains to be seen."
The hostage's brother added: "If it has taken place, then it can only be a positive thing.
"I would much rather be dealing with people talking money than ones holding a government to ransom. Funds can always be found, somehow."
A multi-faith walk dedicated to the captive was held in Liverpool over the weekend.
Representatives of seven major religions toured temples, mosques and synagogues before walking along Hope Street between the city's two Cathedrals in a symbolic act of solidarity.
Mr Bigley's son, Craig, said messages of support from people on Merseyside and across the world had comforted his family.
Leaflet appeal
The hostage's 86-year-old mother Elizabeth is understood to still be in hospital as a result of the stress caused by her son's captivity.
Over 100,000 leaflets from Mr Bigley's family pleading for his release were distributed in Baghdad on Friday.
British Muslim leaders have also appealed to his captors in the pamphlet, saying the kidnap is not consistent with the Islamic faith.
An Islamic website has quoted an imam who claims to have met the hostage in Baghdad.
The imam Syed al-Kareem, who claims to have met Mr Bigley on Saturday, says one reason why Mr Bigley has not been killed is because his kidnappers are trying to determine whether he is Irish or British.
Their reported doubts stem from the fact that Mr Bigley's mother is Irish.