The situation will continue to be monitored, the source told PA News.
Buckingham Palace would not confirm or deny that the Queen has contracted coronavirus after meeting Prince Charles.
Charles, who first fell ill with Covid-19 in 2020, was said to be “deeply disappointed” to have to pull out of engagements in Winchester after a positive test on Thursday.
A message on his official Twitter page read: “This morning the Prince of Wales has tested positive for Covid-19 and is now self-isolating.
“HRH is deeply disappointed not to be able to attend today’s events in Winchester and will look to reschedule his visit as soon as possible.”
He will now need to self-isolate under current rules for 10 full days, but he could be free after five days if he tests negative on day five and day six.
Camilla tested negative on Thursday morning and continued with a busy day of solo engagements in London and Buckinghamshire, speaking for the first time of how she “very honoured and very touched” to be endorsed by the Queen as a future Queen Consort.
The prince’s diagnosis comes just days after the 95-year-old monarch marked her Platinum Jubilee by expressing her “sincere wish” that her daughter-in-law will be Queen Camilla at Charles’s side when he becomes King.
On Wednesday evening, Charles met scores of people and was accompanied by Camilla at a reception in the British Museum to celebrate the work of the British Asian Trust (BAT).
The duchess, meanwhile, visited Paddington Haven sexual assault referral centre and the Nourish Hub community kitchen in west London, and the Thames Valley Partnership charity in Buckinghamshire.
At the British Asian Trust reception, Charles spoke about the “devastating impact” the pandemic has had on south Asia.
Using his pet name for Camilla, which means “darling” or “beloved” in Urdu, he said: “I cannot quite believe it is almost two years to the day that both my mehabooba and myself were able to be with all of you to celebrate the work of the British Asian Trust.
Charles was in close contact with Chancellor Rishi Sunak, Home Secretary Priti Patel and former Liverpool footballer Ian Rush.
A spokesperson for Sunak said the minister had tested negative for COVID on Thursday.
The prince first caught Covid-19 in March 2020. He suffered a mild form of the virus and described how he lost his sense of taste and smell.
Covid reinfections – where someone tests positive for the virus more than 90 days after a previous positive result – currently represent around 10% of daily cases in England.
Of the 14.8 million infection episodes in England since the start of the pandemic, some 588,114 (4.0 per cent) are likely reinfections.