Michel Barnier said the UK cannot rejoin the EU single market without accepting free movement of people. Burnham has named single market membership as one long-term option.
4 freedoms are required for single market membership, Barnier said: goods, services, capital, people.
£5bn annual UK rebate would not return, Barnier said.
Burnham told the BBC rule-taking is where Britain has ended up.
Barnier said the door is open, but rejoining is the UK's choice.
Why it matters: Burnham argues closer EU ties would cut food prices and help families. He says voters will make the final call on full membership.
Bank of England Governor Andrew Bailey said more open EU trade would boost UK growth.
Conservatives estimate a reset could cost the UK £23bn over a decade.