Prime Minister Theresa May rebuked her finance minister, Philip Hammond, on Thursday after he suggested Britain would only move "very modestly apart" from the EU's economy after Brexit.
Meanwhile backbench MP Jacob Rees-Mogg, who leads a group of more than 50 Brexit-supporting Conservative MPs, warned ministers against being too "timid".
Tensions are rising as the other 27 EU countries prepare to approve guidelines next week for talks on the terms of a two-year transition period requested by Britain after Brexit.
They will be followed by discussions on Britain's future trading relations, but -- just over a year from Brexit in March 2019 -- London has yet to set out exactly what it wants.
In his speech Friday, Davis will promise: "As an independent country, no longer a member of the European Union -- the United Kingdom will once again have its own trading policy.
"For the first time in more than 40 years, we will be able to step out and sign new trade deals with old friends, and new allies, around the globe."
He will say that Britain will be able to negotiate and even sign deals during the transition period, although they will not come into force until afterwards.
Davis denied claims this week that Britain will be a "vassal" of the EU during the transition, when it will follow the bloc's rules in return for market access but have no policymaking role.