If this happens, it will be the first ever across-the-board freeze or cut in the minimum wage and would hit millions of households across the country.
According to the Daily Telegraph, the Government has told the Low Pay Commission, which sets the minimum wage, that it must formally consider its impact on "employment and the economy", before agreeing future increases.
If the current economic uncertainty continues, the millions of people currently paid the minimum wage could therefore lose out.
The national minimum wage is established by law and is traditionally announced in March every year by the Commission, after negotiations with employers, unions and the Government before coming in later in the year.
Last autumn, for example, the rate for those aged 21 and over increased from £6.08 an hour to £6.19 an hour, while the hourly rate employees aged 18 to 20 were frozen at £4.98.
However, employment minister Jo Swinson said in February: "The level of employment is now above its pre-recession peak, but the employment rate is below the pre-recession peak.
The revelation that ministers are now considering the prospect of cutting these hourly rates back down again will come as a further blow to families already reeling from the huge changes to the welfare state that came in yesterday.
But small firms, many of which are struggling due to the economic climate, might well welcome such a move.
Figures indicate that eight out of 10 small shops have had to lay off staff in the past year because of rising costs, while off licence managers are known to support the freezing of the minimum wage at its current level.
According to the Financial Times, the minimum wage was established by the Labour government in 1999 at a rate of £3.60 an hour.