Chief executive Sean Doyle said the airline has received “an awful lot of interest” from people planning trips to reunite with their loved ones.
Mr Doyle added that he expects travel restrictions to be eased for countries which are “vaccinating at pace.”
“The US has vaccinated 59 per cent of all adults, and infections are falling, so we’d be very optimistic about the United States,” he said, adding, “And if we look at places like Germany and you look at France, again they’re making great progress, as is Europe.”
“So we think Europe and the US certainly should be in scope for inclusion in the green list as we see the trends on vaccination and prevalence,” Mr Doyle told the broadcaster.
Portugal, one of just a handful of destinations on the Government’s quarantine-free green list, will welcome 16 flights from England at Faro Airport in the Algarve on Monday.
Tui is using aircraft normally reserved for long-haul routes to accommodate the surge of passengers.
But Sir Jeremy Farrar, director of The Wellcome Trust charity, warned there “is a risk” that the coronavirus variant first identified in India could be transmitted by people travelling out of the UK.
“I think travel should still be very cautious and only when absolutely essential,” he told BBC Radio 4’s Today programme.
This comes after Health Secretary Matt Hancock said on Times Radio that destinations on the amber list – which includes Spain, France, Italy and Greece – are “places that you shouldn’t go to unless you have an absolutely compelling reason.”