As tensions with Brussels soar over the implications for Northern Ireland, May will also emphasise that Britain wants to be "good friends and neighbours" with the EU, a minister said.
In a much-anticipated major speech, just weeks before trade talks are due to start in Brussels, May will argue Britain must forge its own path free from the bloc's current rules.
But she will call for the "broadest and deepest possible agreement, covering more sectors and co-operating more fully than any free trade agreement anywhere in the world today".
May will say this is "achievable" because "rather than having to bring two different systems closer together, the task will be to manage the relationship once we are two separate legal systems".
EU leaders have been pressing the prime minister to clarify what she wants before they agree their position on the future economic partnership at a summit later this month.
Brussels raised the pressure this week with a draft treaty suggesting Northern Ireland could stay in a customs union with the EU while the rest of Britain remained outside.