The flag, used at Best's funeral in 2005, was due to be sold at auction on Wednesday by lan Best.
It was expected to raise around £6,000 but the lot did not sell during the initial auction process.
Auctioneer Bonhams is still in discussion with potential buyers.
lan (43), who lives in Torquay, Devon, owns the flag but his decision to sell it has reportedly caused a row with family and friends back home in Northern Ireland. One friend has described the sale as “macabre”.
The Northern Ireland Football Association flag was draped over the coffin on the journey from his father's house to the Manchester United hero's final resting place at Roselawn Cemetery, Belfast, on November 25, 2005.
lan said he is just part of a normal working class family, adding “there are no airs and graces”.
He originally put the flag up for auction in October 2008 but it was later withdrawn. He said the choice to put the flag on George's coffin was made by his father out of respect for the country.
He says he was “very close” to George despite there being a 20-year age gap. He said: “People have this idea that because we are part of George's family we have money, but we don't.”
lan was made redundant last year but has since found a new job.
The flag has been estimated as being worth up to £6,000.
One of George's friends, 65-year-old Malcolm Wagner, called the sale “macabre”, and said the flag should go to the Manchester United museum or the George Best Foundation, which was co-founded by George's sister Barbara McNarry.
But lan has said his only motivation for selling the flag — which he says George never had any contact with — was to buy family heirlooms from his dead father's estate in Northern Ireland.
“The flag was draped over his coffin but that was it, and I wanted to use the money to buy things that were closer to George,” said lan.