The issue of the partial privatisation is contentious within the Labour party, and the delay could be a way of appeasing backbench rebels.
Legislation that would allow for the sale was meant to be passed before the summer recess but reports say it is likely to be put back until the autumn term.
At the moment, only one bidder is left in the running -- CVC, but its reported £2bn bid is thought to be too low.
However, Royal Mail has warned that its final salary pension scheme might be closed to existing members if a deal is not pushed through.
It is estimated that the scheme will be £10bn in deficit after a review due to be published later this year.
Any closure of the scheme is likely to lead to strikes among the 150,000 workers enrolled in the scheme.