Harry and Meghan are on Vancouver Island preparing to forge a new life for themselves and their eight-month-old son, Archie Mountbatten-Windsor, after stepping back from royal duties.
It is unclear who will foot the bill for the family's security arrangements when they officially leave the monarchy in the spring.
A former Home Office minister warned the British public could face an "enormous bill" while it has also been speculated a "cost-sharing" deal between the UK and Canada could be agreed.
However, such an arrangement would be opposed by Laurel Collins, who is the MP for Victoria, where Harry and Meghan are staying.
She told the PA news agency: "Yes, I hope that they're planning on covering their security costs.
"When it comes to the money our government spends and taxpayer money it's important that we put this into context and think about our priorities.
"That we're prioritising making life more affordable for people, that we're prioritising protecting our environment and that we're spending our tax dollars on the things that really matter to Canadians."
Ms Collins added she wanted to focus on young families in the area, who "might be struggling with the housing crisis or struggling with affordability".
She added: "I want to make sure we are thinking about our priorities."
Security for the Royal Family as a whole costs the taxpayer in excess of an estimated £100 million a year, but the actual figure is never disclosed.
Harry and Meghan will earn their own money when they step back fully from royal life.
They had initially hoped for a dual role, supporting the Queen, the Commonwealth and Harry's military associations.
However, the idea was deemed unworkable.
The Prince of Wales will offer some private financial support to Harry and Meghan but it is not known if this will come from his £21 million a year Duchy of Cornwall income or other private funds.
Harry joined Meghan and Archie in Canada on Monday night as they prepare to live a more private life.
There appeared to be a subdued response to the new arrivals, with one local business owner saying the people of Vancouver Island are a lot more laid back than their British counterparts.
Vancouver Island, an area known for its outstanding natural beauty, is off Canada's west coast and is part of the province of British Columbia.
On Tuesday the Sussexes issued a legal warning to the media after various outlets published paparazzi shots of Meghan walking her dogs with Archie.
The images of the duchess emerged on Monday morning and showed her walking her two pets with her son in a baby sling in a park in Vancouver.
But the pictures were reportedly taken by photographers hiding in bushes with long-lens cameras.
After the images surfaced, the couple's legal team at Schillings sent a legal notice to the UK press, TV and photo agencies warning against using them.