Deals for air bridges with a "small number" of countries with low Covid-19 levels are expected to be announced on June 29.
The move would mean tourists could go abroad to these countries from 4 July without having to spend 14 days in quarantine on their return.
Foreign travellers would also be able to enter the UK without having to self-isolate for two weeks on arrival.
The BBC reports that one country at the centre of negotiations is Portugal.
The government, which earlier said restrictions will be reviewed every three weeks, has been under mounting pressure from the tourism and hospitality industries to ease restrictions.
However, the BBC reports that a senior aviation source has said restrictions in relation to those countries without air bridges are expected to be in place for the remainder of the summer.