Britain is "not going to compromise on the fundamentals of having control over our own laws," Frost said ahead of an eighth and final round of scheduled negotiations with the bloc next week.
"We are not going to be a client state," he told the Mail on Sunday as the stalled talks with the EU near their conclusion.
Britain followed through on the results of a 2016 EU membership referendum and officially pulled out of the bloc in January after nearly half a century.
But a standstill transition period that ends on December 31 allows the UK to effectively function as if it were still a member.
London and Brussels are supposed to agree new trade terms in the meantime that prevent ties from reverting to the minimum standards -- and accompanying high tariffs and quotas -- of the World Trade Organization.