Reporting the data on Sunday (20 June), The Telegraph suggests fully vaccinated adults will be allowed to travel to amber countries with their children without having to quarantine under plans being drawn up by Department of Transport officials.
The move would allow families to travel to European countries which are currently on the amber list, such as Spain, France, Greece and Portugal.
The paper further reports ministers could consider the plans later this week, but are not expected to introduce any changes until August.
The next formal review of the traffic light system is set for 28 June, with details expected later this week.