Ministers are facing increasing pressure to move India onto the “red list” of hotel quarantine countries.
Some Top UK scientists have said they expect the new Indian strain of the virus to become a "variant of concern".
It comes just days before Boris Johnson is due to visit the country as part of his post-Brexit trade drive.
Last week Downing Street said the trip would be “slightly shorter” than planned and most of the important meetings are due to take place all on one day – Monday 26 April.
Asked if the Prime Minister should still be travelling to the country, Housing Minister Christopher Pincher told LBC: “Well, India is a hugely important business and cultural partner.
“The prime minister himself has had covid, he knows exactly what it means to suffer from that terrible illness.
“We are making sure that the arrangements are Covid- secure so that that visit can take place safely.
“But of course, it will be kept under review as all these visits are as events unfold.”
More than 70 cases of the variant, which has a “double mutation”, have been identified in England and Scotland.
Some cases have been found in the UK that were not linked to travel.
Dr Susan Hopkins of Public Health England said yesterday that they were investigating the strain but did not yet know if it had increased transmissibility, severity or vaccine evasion.
Labour has already urged the PM to “set an example” and cancel his trip because of the Covid risk.
Steve Reed, the shadow communities secretary, told Sky’s Sophy Ridge on Sunday: “I can’t see why the Prime Minister can’t conduct his business with the Indian government by Zoom.”
Danny Altmann, professor of immunology at Imperial College London, told Good Morning Britain: "My assumption from everything I've seen is that it will become a variant of concern. When it becomes a variant of concern, I'd be quite surprised if India wasn't on the red list."
Andrew Hayward, professor of infectious disease epidemiology at University College London said his preference was to "err on the side of caution and act sooner rather than later", but that the decision was a political one.
However, Dr Jeffrey Barrett, director of the Covid-19 Genomics Initiative at the Wellcome Sanger Institute, said that the variant should be "watched carefully" but it is "probably not at the top tier of mutations that generate the most concern."