Britain is on track to sell shares in Royal Mail at the top of its range, two sources close to the deal said.
This values the postal service at £3.3 billion on the final day that investors can put in orders.
Despite the threat of strike action from delivery staff and criticism from opposition lawmakers, the government is close to completing the sale of a majority stake in the near 500-year-old Royal Mail.
This is its fourth attempt to sell off the postal service.
The privatisation, which at the top of the expected price range would value Royal Mail at £3.3 billion, is the UK's biggest since John Major's government sold the railways in the 1990s.
The stock market offering has received strong demand from the outset, and investors have now been told those with orders below 330 pence per share, the top of an original 260p-330 pence range, risk missing out, the sources said.
Investors have also been warned that, due to strong demand, they should expect their orders to be scaled back.
The financial spread betting firm IG is predicting the shares could close between 385 pence and 405 pence on their stock market debut on Friday.
IG Chief Market Strategist David Jones said the success of past big privatisations such as BT and British Gas was probably attracting retail investors.
"People have got memories about how well these government sell-offs did back in the 1980s and 90s," he said. "With those, there were decent windfall profits on the first day."
Despite the strong demand, many members of the public are against the sale, with a YouGov survey in July showing two-thirds of British adults opposed the privatisation.
The government has said around 30% of the shares on offer are expected to go to individual members of the public ,who must spend a minimum of £750 to invest in the company.
It has also agreed to hand 10% of Royal Mail's shares to staff in the largest share giveaway of any major UK privatisation. If they are distributed equally among the 150,000 eligible UK-based workers, each could receive £2,200 worth.
The sale of Royal Mail follows the flotation of its Belgian peer bpost in June and comes as strong equity markets have helped to revive new listings in Europe this year. European flotations raised $15.9 billion in the first nine months - three times the level a year ago, according to Thomson Reuters data.
Vodka maker Stock Spirits today began taking orders for its London share sale, while the debt collection firm Arrow Global saw its shares open higher on their London debut.