UK passport control at Heathrow Airport. Photo: Daniel Leal-Olivas/AFP
The prospect was raised by the UK's Daily Telegraph newspaper on Sunday.
If the UK reviews Denmark's travel corridor status this week, that means that travellers from Denmark to the UK will need to self-isolate for 14 days.
Denmark was exempted from the UK's quarantine regulations on July 4th, when the country brought in its first travel corridors for low-infection countries.
The risk to Denmark's status comes as travellers from Sweden were on Saturday exempted from the UK's quarantine requirement following a sharp drop in its seven-day infection rate.