Burnham's comments came after he told his ruling Labour Party's annual conference that he would set out "different options" for future ties with the European Union closer to a planned summit with the bloc later this year.
Britain voted to leave the bloc in the contentious 2016 Brexit referendum.
Burnham, who campaigned to stay in the EU, has previously said he hoped Britain would return to the 27-nation bloc within his lifetime.
Options that could be looked at now included joining the European single market and customs union, "or we could go all the way", he told BBC Radio's Today Programme.
"So there are clearly options that need to be considered, and we have to look at what is doable, and what would be the pros and cons of each.
"What I am saying is it's not good enough to leave that question just hanging," he said.
Burnham, who has been prime minister since July, told the Labour conference in his leader's speech that Brexit had triggered "a decade of low growth which has put us in a weaker position".
"We will not give Britain the clear path we need into the rest of this century until we decide on a long-term relationship with what is still our largest market," he added in the speech Tuesday.
The summit with the bloc had been due to be held in July in Brussels.
But that plan was derailed when former prime minister Keir Starmer was ousted as Labour leader and replaced by Burnham.
The Financial Times reported Wednesday that November 20th had now been pencilled in for the summit, although the date has not been confirmed.
READ MORE: What's on the agenda at the next EU-UK summit... if it takes place?
The two sides had been hoping to present several deals at the summit, namely on food and animal safety standards, a youth mobility scheme and the linking of their emissions-trading systems.
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