Hussain Bisad might need "urgent" medical help
Hussain Bisad, who stands at 7ft 9in tall, says he is now due for the title, overtaking the current holder Tunisian Radhouane Charbib, who stands at 7ft 8.9ins tall.
The 27-year-old Somalian, who has been living in London since last year, has size 26 feet, weighs 33 stone and has to sleep in a 9ft long bed.
To claim his place in the Guinness Book of Records, experts must now verify his height.
Tallest Somali
After fleeing civil war in his home country, Mr Bisad now lives in Neasden.
On Monday, he told a national newspaper: "I'm still growing and getting taller every year.
"I'm proud to be the tallest man in the world and proud to live in England."
Doctors have, however, expressed concerns about Mr Bisad's health, especially if he is still growing.
A Guinness Book of Records spokeswoman said Mr Bisad was measured last September.
"He was just over 7ft 7in tall, which made him the tallest man in Somalia," she said.
"Now he's saying he's grown an inch-and-a-half more, which would give him the record.
"We would advise him to come into our offices, get his height checked again and see if he really is the world's tallest living man."
Mr Bisad came to Britain as an asylum seeker after robbers shot him in the knee in Somalia.
He travelled by lorry to Ethiopia before getting on a plane to the UK, where airline staff had to allocate him two seats.
The Home Office has now given him permission to stay in Britain indefinitely because he is deemed a legitimate asylum seeker.
On Monday, Dr Mike Besser, a professor of medicine, who recently retired from St Bart's hospital in London, said Mr Bisad may have a tumour of the pituitary gland.
He said: "A height of 7ft 9ins is difficult to conceive as being simply tall. The majority of people who grow above about 6ft 6ins are normally suffering from a 'pituitary giantism' or tumour.
'Strict checks'
"He needs urgent medical help because the tumour can cause things like blindness, or worse."
Mr Bisad said he was enjoying the attention his size was attracting but confessed to having problems squeezing through doors and fitting into phone boxes.
He had admitted not even attempting to use the London Underground.
The spokeswoman for the Guinness Book of Records added: "The measurement process is very strict and involves heights being taken at different times of the day and night by a qualified medical practitioner.
"We will be delighted to measure Hussain."
The world's tallest ever man was American Robert Wadlow, who died in 1940, at 8ft 11ins.