The government is planning to relax its travel quarantine rules in early July for some countries.
Talks are taking place between UK officials and those in a number of European countries, including Portugal.
However, the UK hopes to make an announcement on 29 June that it has secured a number of “travel corridors”.
The government had previously said that the quarantine would be reviewed every three weeks and 29 June marks the end of the first three-week period.
A travel corridor would mean that two people travelling in both directions between two countries would not have to self-isolate after they travel.
A senior aviation source has told the BBC that the quarantine could remain throughout the summer for anyone arriving from countries which do not have a travel corridor with the UK.
Portugal’s foreign minister previously said that anyone in the UK thinking of going to Portugal this summer would be “most welcome” despite the coronavirus pandemic.
Augusto Santos Silva said he hoped an “air bridge” between the UK and Portugal could be secured by the end of June.
However, the broader travel quarantine is expected to remain in place.
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Anyone arriving from the Republic of Ireland, the Channel Islands or the Isle of Man does not have to complete a form or enter quarantine upon arrival in the UK.
There are also exemptions for workers in some industries such as road haulage and medical professionals who are providing essential care.
The travel industry has been vocal in its criticism of the government’s quarantine rules, warning that the isolation period will deter visitors and put jobs at risk. Some airlines were in the early stages of legal action.
The manufacturing industry has also highlighted that fewer flights will restrict imports and exports, which will have a knock-on effect for the freight industry, as well as hampering the recovery of some businesses.
Despite criticism from businesses, Home Secretary Priti Patel said that the measures were “proportionate” and being implemented “at the right time” when they came into effect on 8 June.