Speaking to Radio 4’s Today programme, Reynolds said current discussions ahead of the summit are around food and drink, electricity and emissions trading.
He said: “What the prime minister has also said, quite rightly, is we face a series of policy changes on the European side that will affect us.
“We need to get as little uncertainty as possible, we need to have a way to resolve what our long-term relationship will be and he is going to set that out after the summit.
“He is going to be frank with the British people about what the trade-offs are but no assumptions have been made on that.”
Pressed on whether UK officials are talking to the EU about freedom of movement Reynolds said: “They will be talking to them about what the future options for our relationship might be.
“But here and now, the focus should be on the summit and the tangible difference improvements we’re going to make.”
Burnham is far more willing to have a public conversation around Brexit than his predecessor Sir Keir Starmer, whose government was nervous about reopening a debate that proved so contentious in the past.
Some people within the Labour Party had been urging Sir Keir to go further and there is a widely held view that Burnham’s comments are likely to go down well with voters tempted by the Liberal Democrats and Greens.
But there is nervousness among Labour MPs with small majorities in Brexit-supporting, Reform-facing constituencies.
Labour MP Melanie Onn, whose constituency Great Grimsby and Cleethorpes backed leaving the EU, told the Today programme Burnham risked losing trust by talking about going beyond the 2024 manifesto at a future election.
“I don’t think that the scars have healed for many people around the country so I do think this is an unnecessary conversation to be having at this time,” she said.
Onn, who lost her seat in 2019 to the Conservatives but won it back in 2024, warned against re-opening the conversation, saying: “Trust is incredibly important, it’s hard-earned and easily lost, and on this matter I think that we should tread incredibly carefully.”
Reform UK leader Nigel Farage told Breakfast that “Andy Burnham has no mandate to be in Brussels, to be negotiating any of this” and called for the prime minister to put his ideas to the public in a general election.
On Monday, Burnham left the door open to a potential referendum on freedom of movement with the EU.
The prime minister caused some confusion when he told broadcasters that he would not reintroduce free movement without a referendum, but Downing Street later said no decisions had been made on whether a public vote would be needed.
Housing Secretary Angela Rayner told the on Sunday that no options for the UK’s future relationship could be taken off the table.
But Burnham did appear to draw some red lines of his own when he told the Sunday Times, external that he would not be in favour of the UK joining the euro or the border-free Schengen zone.
The fact the prime minister has not been willing to say the same thing about free movement is being seen in Westminster as evidence that he believes it is a genuine option.