The call comes from Glasgow South West MP Ian Davidson, who lost the Scottish Labour deputy leadership race in 2011.
Party leader Mr Miliband wants to scrap the electoral college system for electing the leader, whereby MPs, party members and trade unions each get a third of the vote, and replace it with a one-member, one-vote system.
Scottish Labour has the same electoral college system under which MSP Johann Lamont was voted leader and MP Anas Sarwar her deputy.
Asked if it would adopt the reforms proposed for the UK party, a spokeswoman said: "We will probably do the same but we will have to look at the proposals and make a decision."
Mr Davidson, who won the trade union section of the deputy leadership ballot but lost in the MPs' and party members' sections, believes Mr Miliband's proposals are a bid to loosen if not break Labour's link with the trade unions. He also questioned whether at a time of a cost of living crisis, an indepen-dence referendum and two elections, it should be focus-ing on internal structures.
The Labour back-bencher, who chairs the House of Commons Scottish Affairs Committee, said: "The Scott-ish Labour Party should be considering what its priorities are and not blindly following what is done in the UK as a whole. If the change is adopted, it seems logical that the existing leadership should put themselves up for re-election under the new system."
Among the planned changes, which will be voted upon at a conference in London on March 1, is one relating to affiliation fees.
The proposal is that individual trade unionists will no longer be automat-ically affiliated through the payment of the political levy by their union but will be able to take part in elections if they choose to join an affiliated members category.