Alex Rowley, the party’s constitution spokesman, said the “option of the [referendum] power sitting in the Scottish Parliament... is worth serious consideration”.
Currently the power to hold a referendum has to be transferred by a Section 30 Order from Westminster to Holyrood. It is this order which Boris Johnson has refused to grant despite demands by First Minister Nicola Sturgeon that the general election result gave the SNP a mandate to hold indyref2.
A former deputy leader of Scottish Labour, Mr Rowley has long been an advocate for "home rule" - a position recently touted by his party's leader Richard Leonard - and has now produced a pamphlet discussing his views on independence and a second referendum.
He says that Scottish Labour needs to diverge from the unionism of the Conservatives and the "illiberal" Liberal Democrats, that it is "the sovereign right of the Scottish people" to decide the country's future, but stops short of backing independence.
Mr Rowley is the second senior Scottish Labour member to push for a change in the party's policy on a second independence referendum. Shadow health spokeswoman Monica Lennon has also said the "future of Scotland must be decided by the people of Scotland".
His idea of "home rule", he says, would result in further substantial powers being devolved to Holyrood - leaving areas such as macroeconomics, defence and foreign policy in Westminster. The whole issue, he says, should be put to members of the Scottish Labour Party and not decided by a "small band of MSPs".
Mr Rowley writes: "There are some within the Scottish Labour group who want us to rule out any referendum for the foreseeable future. This would put us alongside the Tories and illiberal Liberals and would play direct into the hands of Nicola Sturgeon."
He also says that while he does not believe the Scottish Government has a mandate for another vote, the issue is not one that should be determined by Westminster. "My own view is that the option of the power sitting in the Scottish Parliament with a requirement of a two-thirds majority to trigger any future referendum is worth serious consideration."
Votes from 85 MSPs would be needed to make up two-thirds - meaning pro-union voices would have to be persuaded to supplement the 68 independence-supporting MSPs from the SNP and Scottish Green Party.
However he also claims the First Minister is "not serious" about holding another vote this year, a position she has this week stood by despite the Prime Minister's rejection of the powers to hold another referendum.
Mr Rowley suggests the SNP was looking to make the 2021 Holyrood election into a vote on Scotland's constitutional future - something he claimed was a "deliberate deflection tactic" from the party's record in government.
He added: "We should also be clear that Labour supports the sovereign right of the Scottish people to determine their own future and we should not weaken that position by being caught in this false argument about another referendum.
"Right now in Scotland there is no majority demanding a referendum so let us focus on our vision for Scotland."
Despite Mr Rowley's direct contravention of Labour policy, the party's Scottish leader Richard Leonard welcomed his pamphlet.
“Scottish Labour’s executive has commissioned a review into the general election result and the lessons we can learn from our defeat. Candidates, elected representatives, party members and affiliates are contributing their own views during this period, and I will consider these alongside the shadow cabinet and Scottish Labour’s executive," he said.
“Scottish Labour is opposed to the creation of a separate Scottish state, and we are opposed to the SNP’s vision for a decade of cuts after independence. We believe that home rule for Scotland within the UK, with more powers not just for the Scottish Parliament but for every workplace and community, offers the greatest opportunity to bring about real economic, social and environmental change.”
SNP deputy leader Keith Brown accused Labour of attempting to "block democracy". He said: "Labour always seem desperate to create new schemes and wheezes to block Scottish democracy.
"This latest plan is reminiscent of the infamous 40% rule in 1979 - where Labour conspired to block a Scottish Assembly despite a majority of Scots voting for one.
"While it's welcome that figures in Labour are increasingly realising that Scotland's future must be for the Scottish people to decide, they need to ditch this plan to tie Holyrood's hands."