Amazon's promise of next-day deliveries could be investigated amid customer complaints that it is failing to meet that pledge.
The UK Advertising Standards Authority (ASA) is considering whether to launch a formal inquiry into Amazon.
The firm's top service, Prime, offers next-day deliveries for £7.99 a month.
The ASA said: "We have received a handful of complaints about Amazon parcel deliveries and we are at the initial assessment stage."
An Amazon spokesman told the BBC the ASA had confirmed to it there was no investigation at this time.
The ASA said there had been five complaints since the start of the month.
Amazon offers free delivery above a certain minimum spend, but express, unlimited delivery for Prime customers.
It also offers this coming Saturday, 23 December, as its final order date for Christmas orders, three days later than the Wednesday offered for non-Prime customers.
Amazon Prime customers who contacted the BBC reported mixed experiences.
Gary Nicholson, from Farnham in Surrey, said: "Our Amazon Prime deliveries often miss their 'next day' target. We always make a point of complaining, and are generally given a 30-day extension to our annual subscription."
Dr Guy Simmons also emailed in. He, too, had experienced missed deliveries, but said it was unreasonable to expect perfection every time: "I have had Prime for years. It has been very rare indeed for a parcel not to arrive by the guaranteed date. On those occasions, Amazon has extended my Prime membership by one month.
"It is a fantastic service and it is totally unreasonable to expect that things may rarely not work out."
Amazon advises customers to contact customer services if they do not receive a parcel by the estimated delivery date.
The consumer rights group Which? points out that a company missing its delivery date is in breach of contract.
It says that consumers have the right to terminate the purchase and get a full refund in that instance.
It says the first step should be to contact the retailer directly to make a complaint that a parcel has not been delivered and request they take action to remedy the situation.
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