According to the Times, the Department for Transport has been told to draw up a paper on the proposals, which will be discussed at a meeting of the Covid-19 operations committee (Covid-O) next week.
The proposal will be considered as part of a review of the travel traffic light system, due at the end of June.
The policy change would mean the return of quarantine-free holidays to holiday hotspots including France, Italy, Greece and Spain which are currently on the amber list.
The paper reports that if the new system is approved, it will not be introduced until late next month or early August.
Sources said that this is due to a number of issues that need to be ironed out, including the status of un-vaccinated people and the treatment of non-British visitors arriving in the UK.
However, travel industry bosses want the change to be introduced by July 1 to coincide with the launch of the EU “digital Covid certificate”, which will let vaccinated people or those with a negative test travel freely in the bloc.
As of now, 12 EU countries including Austria, Belgium, Greece and Spain are using the app to provide digital proof via a QR code that a traveller has been vaccinated against Covid-19, has recently tested negative for Covid-19 or has recovered from the illness.
The government confirmed this week that it was exploring whether double-jabbed Britons could be given the go-ahead for holidays in “amber list” countries without quarantine on return.
Jesse Norman confirmed that “this is one of those things that is being considered,” adding that “we don’t want to get left behind by countries which may be adopting a two-jabs approach if it can be done safely, carefully and securely.”
However, Mr Norman added: “We are trying to move cautiously and progressively in the right direction so I wouldn’t write anything off at this point.
“But then, you know, we are in a situation where the...virus is not something we control and we have seen this new Delta variant and therefore, it would be imprudent to make any carte blanche or, as it were, firm statement now.”
People in the UK are currently advised not to travel to amber list countries — such as Spain, France, Italy, Portugal and the US — apart from for a limited number of reasons such as attending a funeral.
On their return they must quarantine at home or in the place they are staying for 10 days, taking a Covid-19 test on or before day two and on or after day eight.
They can also pay for an additional test after five days which if negative means they can get early release from quarantine.