The MEP for the South East of England argues a similar arrangement would not take seven years to negotiate and ratify as we are starting from a position of zero tariffs.
Writing in The Sun, Mr Hannan said: “Our geography pulls us towards a deal that looks more like Switzerland’s than South Korea’s.
“We should aim to work with our neighbours in areas such as policing, intelligence and research, not just trade.
“But we should do so as an ally, not as a province.”
Canada’s arrangement with the EU means it trades without any tariffs except in farming – and even then the tariffs are low.
It also recognises many professional qualifications.
Mr Davis hopes to go further than Canada on financial services, keeping banking, insurance and investment arrangements similar to what is currently in place.
But while the EU27 would gain as much as the UK from this kind of arrangement, Britain does not know yet what the bloc wants in exchange.
Mr Hannon argues getting a deal similar to Canada’s, known as CETA, would not take as long to sort out.
He said:“It is often pointed out that Canada’s trade deal with the EU — known as CETA — took seven years to negotiate and ratify.
“Indeed it did and one of the arguments for leaving is that we can now sign trade deals more quickly with the US, China, Australia and so on.
“The parallel is meaningless in this case. What takes time is agreeing new arrangements. In our case, we are starting from a position of zero tariffs and identical regulations.
“There will be areas where we wish to opt out — for example, we want to be able to buy food at world prices instead of under the Common Agricultural Policy.“
The MEP says it is important that we strike out own deal, based on what is best for Britain, but we need to work as an independent country that is in close cooperation with its neighbours.
Speaking on BBC’s Andrew Marr Show, David Davis said Britain has until the end of 2018 to sign a free-trade deal with European leaders.
He said: “It’s more like a year than eight months, in truth – bear in mind we can’t sign this until we actually leave.”
Mr Davis said reaching an agreement would be “not that complicated” thanks to Mrs May’s recent victory in Brussels – and described his preferred solution as “Canada plus plus plus”.
The Brexit Secretary said he wanted a “bespoke” deal with the EU and is aiming for an “overarching” agreement with no tariffs.