The shadow Brexit secretary said his party was not "ruling out" a public vote on the final deal Theresa May negotiates with Brussels.
He also admitted that the UK leaving the EU means "things will get worse" in the short-term.
Jeremy Corbyn has previously dismissed calls for a "People's Vote" on the Brexit agreement but, speaking at a private meeting of the Labour Business Group, Sir Keir said it remained a possibility if Parliament rejects the deal.
Asked what would happen if the final deal is voted down, Sir Keir said: "It is Parliament that should decide what happens next, it should have the power to decide the options, and this might involve a general election or a 'People's Vote'."
He added: "We're not calling for it. We respect the result of the first referendum.
"But we're not ruling out a second referendum."
There is growing pressure on the Labour leadership to support calls for a second referendum, with many party members, the influential Momentum campaign group and a number of MPs ramping up their campaign for the public to be given a say on the final deal.
Earlier in the week, the Unite trade union, Labour's biggest donor, said it was "open to the possibility of a popular vote being held on any deal".
Sir Keir was also asked whether things were likely to get worse once Britain quits the EU.
He said: "Yes, things will get worse in the short term, as impact reports show. But I don't want to tell my kids that it's all downhill from here.
"We have a duty to make [Brexit] work."
The People's Vote campaign welcomed Sir Keir's comments.
A spokesperson said: "Travel inside the Labour Party on this issue is in only one direction.
"This week Unite, Labour's biggest affiliate, made it clear that a People's Vote on the final Brexit deal was a real option for Labour and now the shadow cabinet member with policy responsibility for this area appears to be confirming that view.
"Brexit is a big deal, but it's not a done deal."
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