Grant Shapps, the transport minister, is said to be pushing for the abolition of Passenger Locator Forms in time for the Easter holidays.
According to the Daily Mail, he wants to end the forms by the beginning of April to make it easier for families to fly overseas.
The forms are to be simplified in the coming weeks as an interim measure.
Boris Johnson is due to set out his plans later today to scrap all remaining Covid legal restrictions in England, including the requirement to isolate.
The chief executive of Airlines UK told the newspaper that ministers are right to remove the remaining restrictions, but this needs to cut across all elements of the economy, including travel.
If there is no requirement to self-isolate for those with Covid in the UK, jabbed or otherwise, there can be no justification for continuing with travel restrictions for the unvaccinated.
Shapps hailed the easing of travel restrictions from February 11, saying eligible fully vaccine arrivals no longer need to be tested when arriving into the UK.
PLFs, which need to be filled in before returning to the UK, are a barrier for people who want to travel.
Shapps promises a passenger locator form on Friday.
Booking levels are catching up with pre-pandemic levels.