Raab told Sky News on Thursday (29 July) he was "increasingly confident" more countries would be added to the lists.
His comments come after the UK government on Wednesday (28 July) confirmed it would ease quarantine for fully vaccinated arrivals from the US and Europe.
Raab said the move could potentially open up more countries for holidays, but declined to comment on which countries’ statuses might change.
MORE: Biden administration urged to set timetable to reopen US borders
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The next three-weekly review of the UK government’s traffic light categories is due next week.
Wednesday’s announcement on the mechanics of the UK’s travel rules came days in advance of the second formal "checkpoint" baked into the proposals to restart international travel set out by the Global Travel Taskforce in April.
Raab also revealed that since the announcement on Wednesday afternoon, he’d already been contacted by several of his international counterparts.
"Overnight, foreign ministers [have] messaged me saying we’ve noticed this announcement - what can we do to do this on a reciprocal basis," Raab told Sky’s Kay Burley.
He added it would be vital, however, that there were the necessary levels of "security and assurance" with regards to vaccination schemes in those countries to which the UK will reopen.
The devolved administrations in Scotland and Wales have confirmed they will adopt the same rules as England, as set out by the Westminster government. The Northern Ireland Executive is expected to discuss the matter before the weekend.
Raab added he was hopeful of a broader resumption of international travel "as soon as possible" but cautioned there was yet some way to go to returning to a pre-pandemic travel landscape.
"We won’t get there in one fell swoop, we’ll get there incrementally because that’s the way to do it," he said.
Lobbying effort
Transport secretary Grant Shapps, meanwhile, called on the US to offer a reciprocal arrangement to UK travellers to open up a corridor between the two countries based on vaccination.
The Telegraph reports Shapps having spoken to US transport secretary, Pete Buttigieg, and later commenting: "We can’t change the other side, but we do expect in time they will release that executive order, which was actually signed by the previous president and bans inward travel."
Shapps was referring to proclamation 212F signed by former US president Donald Trump, which still – to this day – largely restrictions travel to the US from the UK and much of Europe.
On Wednesday, several trade bodies – including Abta – called on the US to reciprocate the UK government’s stance. Earlier this month, president Biden had seemingly been gearing up to reveal further details of the US’s plan to reopen its borders, a White House official this week poured cold water on the prospect.
The US is grappling with a fresh wave of Covid infection owing to the delta variant, and is having to reintroduce some mitigations to limit the spread of infection.
