According to the Daily Telegraph, the Whitehall meetings - arranged to avoid political embarrassment - follow concerns that some small investors would lose out.
Business Secretary Vince Cable said around 700,000 applications were made by Tuesday night's deadline, which he believed showed the high level of interest in the controversial privatisation.
Around 30% of shares have been set aside for the so-called retail shares, with others going to institutional investors and staff.
Business minister Michael Fallon said: " No decisions have been taken on allocation but I'm committed to making sure smaller investors get their fair share."
Mr Cable faced tough questions from members of the Business Select Committee amid concerns that the business, and some of its properties, was being undervalued.
Committee chairman Adrian Bailey (Lab, West Bromwich West) said the minister was overseeing the sale of a profitable, popular, publicly owned company to financial institutions he had criticised in the past.
Conservative MP Brian Binley (Northampton South), asked why the Government was "discriminating" against Royal Mail employees who will lose their free shares if they leave the company within three years.
"I suspect Royal Mail will downsize some of its operations within three years, and employees who lose their jobs will lose their shareholding. Don't you feel you are being unfair?"
Mr Cable replied that so-called "good leavers", such as those made redundant or who resign on health grounds, would be protected.
The minister hit back at critics of the sale, including the Labour Party, denying allegations that a number of Royal Mail sites in London were being undervalued.
Asked about the relationship between a privatised Royal Mail and the Post Office, which is remaining in the public sector, he said it was "unthinkable" that it would be diminished, given how much work flowed between the two.
Earlier, MPs voiced fresh concern that the privatisation would be "highly lucrative" for speculators, hedge funds and investment banks rather than the public.
An Early Day Motion was tabled by the SDLP calling on the coalition to review its decision, and warning that the commitment to deliver six days a week could be "watered down".
Conditional trading of shares will start on Friday and full trading next Tuesday, a day before the result of a strike ballot by the Communication Workers Union.
CWU members are expected to back industrial action over issues linked to privatisation, with any strike set to be held on or after October 23 - the run-up to the busy Christmas period.
In written evidence to the select committee, the Government said its main objective was to secure the universal postal service, which guarantees deliveries to every address in the UK, six days a week, for the same price.
The submission said the Royal Mail was on the road to sustainability, with an increase in its operating profit to £403 million.
"Royal Mail must continue the process of modernisation and transformation, and must be able to invest to grasp new business opportunities," said the Government.
"It should be able to access flexible capital so that it can continue to modernise and innovate, invest and seize opportunities presented by new markets such as the rapid growth of online shopping."
Consumer watchdog Consumer Futures warned that "ill-considered" use of measures by the regulator Ofcom could stifle or restrict competition in the postal services market.
The group said there could be a "perverse incentive" on Royal Mail not to address inefficiencies, adding: "Whether Royal Mail is in public or private ownership, Ofcom must remain vigilant in its monitoring of prices and efficiencies to ensure that Royal Mail is not permitted to raise prices without making the cost efficiencies necessary to ensure the sustainability of the universal postal service."
In its submission, the Royal Mail said privatisation will give it flexible access to private capital, which will be a "positive step" for the universal service.
The company noted that the postal sector had changed "dramatically" in the past decade, with fewer letters posted, more competition and an increase in parcel deliveries.
"Change will continue and the company will employ fewer people in the future, whoever owns it. The company remains committed to the overarching objective of achieving this without compulsory redundancies."
The evidence added: "Privatisation will allow the company to innovate, invest, improve our services, win new business, deliver the high quality universal service, and continue to be a very substantial employer in the UK."
The Northern Ireland Assembly passed a motion saying the Royal Mail is a vital public service which should not be privatised and voicing concern that the sell-off "would add to the costs of Northern Irish businesses and consumers if the universal service obligation and uniform pricing are withdrawn".