Boris Johnson is reportedly looking to restore long-haul flights between the UK and far-flung countries such as Dubai and Sydney.
The Sun says the PM has ambitious plans to get EU-wide safe routes restored by the end of June.
The plans are said to also include negotiating deals with countries such as Singapore.
But No10 has stressed that a deal with the US is unlikely as the ban on Brits is unlikely to be lifted soon.
The UK’s controversial quarantine policy is set to be reviewed in three weeks on June 29.
However, No10 does not expect any progress with the US as a travel ban is unlikely to be lifted soon.
It comes as the Foreign Office advice warning against all non-essential travel is expected to be changed.
Ahead of this expected change, a new note has been added to the website, stating: “This advice is being kept under constant review”.
Tim Alderslade, of industry group Airlines UK, said: “The PM’s personal involvement is excellent news and will provide some real momentum.”
It comes as Gatwick Airport is set to reopen its north terminal and extend its operating hours from Monday.
Airlines EasyJet, Wizz Air and Ryanair are among the carriers set to resume travel from the West Sussex airport.
The coronavirus pandemic caused a global collapse in demand for air travel, with airlines forced to ground their planes as borders closed worldwide.
Gatwick, the UK’s second busiest airport, has been hit severely by the pandemic, with bosses saying demand will not return to normal for four years.
Gatwick chief executive Stewart Wingate said: “The recent Government announcement regarding the 14-day quarantine period for passengers arriving into the UK is, in our opinion, already having an impact on the start of air travel recovery.
“We accept the Government’s absolute priority is the protection of public health, but we continue to push for regular, country by country reviews of quarantine regulations, based on medical evidence.”