Bercow said he would not comment on when such a referendum should be held, but said the fact no one under the age of 57 had been able to have a say in whether the UK should remain part of the EU was unfair.
He told The Huffington Post following a speech on digital democracy on Tuesday evening: "I do happen to think that there is quite a strong argument, actually, for there to be a referendum at some suitable point on British membership of the EU, because it seems to me, otherwise, our membership is fundamentally insecure.
He added: "There is a lot to be said for resolving the issue one way or another."
Bercow's comments could prove controversial as by convention the Speaker is supposed to remain politically neutral. The issue of whether there should be a referendum is likely to be a key part of the next general election campaign.
David Cameron has pledged that should he be reelected in 2015 he will hold a referendum by 2017. Ed Miliband has said a Labour government would only hold one if there were proposals to transfer more powers to Brussels.
However Bercow said he was not "frightened by the question" and that it was "perfectly reasonable" for the Speaker to be asked his view on an issue of democratic participation.
"Now I know a lot of eurosceptics want a referendum and are absolutely convinced that when it comes, not only will they campaign for withdrawal, the very hardline eurosceptics, or europhobes, call them what you like, but they are convinced that will be the outcome," he said.
"But there is equally a perfectly respectful case for people who consider themselves very pro-European Union, or at any rate pro remaining within it, for arguing for a referendum as well on the grounds that the matter needs to be laid to rest."
"I often hear people complain they haven't had a say," Bercow said during the Q&A session at the Policy Exchange think-tank. "It's quite a powerful point, because unless you are 57 you have not voted on British membership of the EU. If you are 57-years-old or older you can have voted on British membership of the Common Market. It is 39-years since that referendum took place."
Britain held a vote on whether to remain part of the Common Market in 1975. Eurosceptic Tory MPs, and others, have long been agitating for voters to be given a fresh say considering how much the EU has since changed.
In the past, Bercow has expressed a preference for Britain remaining within the EU. He caused some controversy last year when he said it was "more sensible" for the UK to remain a member.
Bercow also said on Tuesday evening that while he was opposed to referendums on specific policy issue such as pensions, there was an argument for holding them on constitutional issues "particularly where major parties are all of one view".
His comments could prove awkward as Cameron has indicated he will try again to get his EU Referendum Bill through the Commons this year, via a Private Members Bill. Bercow will have the job of impartially overseeing the debate. And there is not a consensus among the main parties in parliament over if and when to hold a public vote.Suggest a correction