Applicants for US visas are required to disclose any history of drug use, which can affect their applications. Lying on the paperwork can lead to penalties, including deportation.
Speculation about where the Sussexes might live has also been fuelled by the possibility of Donald Trump winning the US general election next month.
The former US president, who is seeking re-election, has said previously that if Harry lied on his visa application about drug-taking, then he would take appropriate action if he returned to the White House.
Mr Dampier suggested that, if the tide turned against Harry, then he might be pushed to return to the UK, which he left in 2020. The royal expert also suggested Harry would like to mend bridges with friends and family in Britain.
He argued the situation is made difficult by the fact the Sussexes’ children, Prince Archie and Princess Lilibet, are growing up in the US – on top of the royal couple losing their UK base, Frogmore Cottage.
Experts suggest reports Harry and Meghan have bought a holiday home in Portugal is evidence of the Sussexes’ wish to maintain a base in Europe.
Meghan and Harry’s popularity in Britain has decreased since the couple stepped down as working royals and moved to North America.
Twenty-three percent of those polled in the YouGov’s popularity survey said they have a positive opinion of Meghan compared with 57 percent who reported disliking her. Figures for Prince Harry are 27 percent and 50 percent respectively.
Sources have told the BBC previously that Harry will continue to live in the US with Meghan and their children.
“Well-placed” sources claimed to the broadcaster in September that despite reports Harry feels restless in California, the Duke and Duchess are unlikely to want to relinquish their business and philanthropic projects across the Atlantic.