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Speaking to BBC Radio 4's Today programme, Burnham said he did not want to leave the question of the EU relationship "hanging" and he wanted to be clear on "where we want Britain to go in the next decade".
Asked whether he wanted the UK to rejoin the EU, he replied that he wanted to "look at the options".
He added he had previously advocated such a move within his lifetime, whilst acknowledging it was "not necessarily the case that that is now".
"We could stay as we are. That's definitely an option, if people think this is the right place to stay," he told the programme.
"We could look at what [former Chancellor] George Osborne has said about a customs union, we could look at what the Liberal Democrats said at their conference about the single market, or we could go all the way."
"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," he added.
In his conference speech on Tuesday, Burnham blamed Brexit for a loss of control over both immigration and the economy, telling delegates he did not believe the current relationship was "good enough".
He told activists he wanted to use the rescheduled summit later this year to lay out "different options" for the UK's long-term relationship with Europe.
He promised to "find consensus" on an option to clarify the UK's position, although did not offer further detail of how this would be measured.
In response to Burnham's conference speech, Conservative deputy leader Alex Burghart said: "Labour cannot pin the blame for their disastrous economic decisions on a vote that happened over a decade ago.
"Besides, they are already dragging us into the European Union via the back door with their EU reset."
