Building on previous comments about the need to rethink ties with Brussels, Burnham told the Sunday Times the influx of EU workers into Britain before Brexit posed significant challenges.
"But, at the same time, it was a type of immigration that perhaps wasn't as difficult (as now)," he said.
"Revolving door migration where people would come and then go back is different.
"The balance of migration has changed, hasn't it, since then? I think we've just got to have an honest discussion about those things."
Official data shows long-term net migration in 2025 fell to close to its level before a new post-Brexit immigration system was introduced at the start of 2021.
In September, two months after replacing Keir Starmer as Labour Party leader and prime minister, Burnham said Britain should consider options for its relationship with the EU, including possibly rejoining the bloc one day.
He had previously backed the pledges of Starmer's government, which included no return to freedom of movement - something Brussels sets as a condition for being part of the bloc's single market.
In his interview with the Sunday Times, conducted on October 19, Burnham said the issue of freedom of movement could be part of a broader reset of Britain's relationship with the EU, including on data sharing and migration.
"You've got to see it in the round, rather than just looking at freedom of movement on its own," he said.
Burnham - who is trying to find ways to speed up Britain's economy - is due to meet top EU officials for a summit on November 20.
He said he could not imagine recommending Britain adopt the euro currency or the EU's border-free travel arrangements.
A new referendum would be needed to rejoin the EU but not necessarily to join the bloc's single market or a customs union, the Sunday Times quoted Burnham as saying.
Former conservative finance minister Jeremy Hunt, who campaigned to stay in the EU in 2016, said it would be a mistake to reopen one of the fundamental debates of the referendum.
He said relaxing immigration rules would hurt people in Britain.
"I think it will be a hammer blow to getting people off welfare and into work," Hunt told Sky News.
