"My objective is clear. Not one day should pass after Britain's exit (from the EU) without new regulations in place," Johann Schneider-Ammann told the Blick daily.
"It should be at least as good" as the present deal, he said.
The paper said Britain's international trade minister, Liam Fox, showed strong interest in a deal with Switzerland at this month's World Economic Forum (WEF) in Davos.
British Prime Minister Theresa May has promised to start the two-year process of leaving the EU by the end of March.
The European Commmision has warned London against negotiating any new third-party trade deals as long as it remains an EU member.
But Schneider-Ammann suggested negotiations with Britain could take place "in the background and in parallel with the exit discussions" with the EU.
"I would be personally very happy if we were one of the first countries to conclude a free-trade deal with Britain post-Brexit", he said.
Switzerland is a founder member of the European Free Trade Association (EFTA), created in 1960 as a counterpart to the European Economic Community, as the precursor of the European Union was known.
Britain too was a founding EFTA member but left the group when it joined the EEC in 1973.
The three EFTA members -- Norway, Iceland and Liechtenstein -- are also members of the European Economic Area (EEA) which gives them access to the EU's single market, but Switzerland is not an EEA member.
Asked about relations with the new US administration of President Donald Trump, the minister was cautious.
"We are waiting to see what happens" regarding the Transatlantic Trade and Investment Partnership, negotiations for which have been ongoing since 2013.
He said if a TTIP deal is concluded then Switzerland could join.
However, Trump is widely expected to drop any attempt to seal the accord.