Mr Trethewy, who is being sued by singer Whitney Houston for allegedly posing as her agent, plans to host a gala launch of the airline on 30 March.
He has said that he has the backing of a large French bank, leases on three jumbo jets and will start the service in December under the name Cunard Airways.
However, the Civil Aviation Authority says it has received no applications for licences. Moreover, a spokesman for the Barbadian Ministry of Aviation said: 'I have no knowledge of any application from Cunard Airways, nor do we have any knowledge of Mr Spencer Trethewy.'
Undeterred, Mr Trethewy told the Independent he would have no problem obtaining a licence when he applied. 'You don't get licences turned down if you have the financial backing, and I have the finances in place.'
Mr Trethewy said he decided to launch the airline because of the 'pathetically cheap' cost of leasing aircraft in the current market, and his knowledge of Barbados.
One person approached to become involved in the launch was told by Mr Trethewy that he was a close friend of Wes Hall, the former West Indian fast bowler who is Minister of Tourism in Barbados.
Mr Trethewy gives the name of his company as Digital Development Corporation, the organisation mentioned on his answering machine. There are two companies of that name registered at Companies House. One has been dissolved; the other was formed last month by Gerald Lewin and Michael Holder of a company called Buyview based in Stamford Hill, north London.
Mr Trethewy came to prominence in 1990 when he offered to pay pounds 200,000 to save Aldershot Football Club, then failed to come up with the money. He was most recently in the news when he resisted eviction from a house in Holland Park. He had no comment when asked if he was still living at the house.