Mr Trudeau has assured the Queen that the family will be safe while in his country, with Canada expected to pay around half of the estimated £1million annual bill.
But there are concerns that the large cost could lead to a backlash in Canada and damage the status of the monarchy there, reported the London Evening Standard.
Harry and Meghan are entitled to 24/7 taxpayer-funded protection at home and abroad as members of the Royal Family, whether on official duties or on holiday.
The couple believe this should continue, even though their security bill is close to £1million a year and this could rise further if arrangements become more complex.
But Scotland Yard have privately insinuated that they are not in the position to write an open-ended cheque for round-the-clock security if the couple are living abroad.
It is understood they have launched a review into the issue – and, while the police will not turn their backs on Harry and Meghan, a compromise is needed.
Buckingham Palace, the Cabinet Secretary Sir Mark Sedwill and the Home Office have already discussed the future of the couple’s security.
The £1million-a-year cost of the couple’s security has been brought down only because they have chosen to live in Windsor, which is already heavily guarded.
However the couple will need constant protection, having been subjected to threats from far-Right organisations and because of Harry’s military service in Afghanistan.
Asked about the issue of who will fund their security, Home Secretary Priti Patel told the BBC today: ‘I’m not going to provide any detailed information on the security arrangements for either them or any members of the Royal Family or for any protected individuals – that’s thoroughly inappropriate for me to do so.
‘At this moment in time, right now, the royal family themselves need some time and space for them to work through the current issues that they’re dealing with.’
Last week it was suggested that Harry and Meghan could face a huge backlash from Canadian taxpayers if they are forced to pay for the couple’s security.
Campaigners say the Royal Canadian Mounted Police (RCMP), who are charged with protecting senior officials including the Governor General, must not write a ‘blank cheque’ on potentially millions of pounds worth of protection, while others suggest Harry and Meghan foot the bill themselves.
Aaron Wudrick, from the Canadian Taxpayers Federation, told The Sunday Telegraph: ‘I thought it was very interesting when they used the term ‘financial independence’.
‘The details remain to be seen. There’s always going to be a cost [to the taxpayer] and the public deserves some prudence. I don’t think it’s reasonable to expect us to pay for everything the way we do for a royal visit.
‘If they’re going to make Canada a second home, a good step in the right direction would be to pay for at least part of it, and not rely on taxpayers to fund their entire lifestyle.’
However, experts say that Mounties would be obliged to do give protection for Harry, Meghan and their son Archie, even if the couple still had UK royal protection officers.
‘I don’t believe they can refuse the government of Canada’s security,’ said Larry Busch, an ex-Royal Canadian Mounted Police (RCMP) officer who directed security for world leaders including US presidents and the royal family.
The cost could easily run into the millions of pounds, said Mike Zimet, whose eponymous New York executive security firm has protected clients including US Senator Bernie Sanders and actors Lin-Manuel Miranda and Alec Baldwin.
‘If they want private protection, then a whole machine needs to be built around them,’ said Mr Zimet.
The level of security they need would be defined by a threat assessment, said Joe Balz, president of GloProSec Preventative Services, a Toronto-based security company, and an ex-RCMP officer who has worked with the royal family and other heads of state in the past.
‘There’s always going to be the odd idiot who causes some type of problem,’ Mr Balz said.
In a post on their website, the Sussexes announced they would be transitioning to ‘financial independence’ after ending funding from the Sovereign Grant, but did not go into specifics as to whether this extends to the cost of their security which is paid for by the State.
However, a recent poll conducted two days before the couple’s shock announcement found that more than 60 per cent of Canadians would support the appointment of the Duke of Sussex as the Governor General of Canada.
The mostly ceremonial role, which is to act as the Queen’s representative in Canada, provides both a residence – Government House in Ottowa – and a security detail.
Some 61 per cent of the Canadians polled said they would support having Harry replace current governor general Julie Payette when her term expires in two years.
The poll came despite Harry never having expressed any interest in the post, which has been held by Canadians since the 1950s but was previously held by Britons.