Labour peer Lord Foulkes has said there should be two separate votes - the first one to decide on independence.
If that vote was defeated, a second ballot could be held on further devolution.
Lord Foulkes has tabled an amendment to the Scotland Bill proposing the measure.
The bill - which is designed to implement the proposals of the Calman Commission to increase the powers of the Scottish Parliament - is being debated in the House of Lords later.
Last week, Scotland's First Minister Alex Salmond set out the question he intends to ask in the referendum on independence which he wants to hold in autumn 2014.
However, the SNP leader, who is holding a consultation on the referendum process, has said that he does not rule out a second question on the so-called Devo Max option, which could see Scotland being given fiscal autonomy.
The UK government has insisted that the referendum should be a single question on whether the Scottish people want independence.
Lord Foulkes, who was a Scotland Office minister in Tony Blair's Labour government, said many people were confused about what question or questions would be put on the ballot paper.
The former MP for Carrick, Cumnock and Doon Valley argued it would be better to split the issues.
He said if people in Scotland voted for independence there would be no need for another referendum.
But if the idea was rejected, then a second vote could be held about a month later to decide what extra devolution powers the country should have.
Lord Foulkes told BBC Radio Scotland's Good Morning Scotland programme: "Well there has been a lot of discussion about two questions at the one time on the one ballot paper, or two ballot papers, making the decision simultaneously and that would confuse things.
"The first question is should Scotland remaining part of the UK. If Scotland is going to become an independent country then the question of devolution and the extent of devolution doesn't arise.
"But if Scotland remains part of the United Kingdom then we have a second question which says how much devolution do you want  - I actually want more devolution, I want more fiscal autonomy, full fiscal responsibility.
"But you can't make a decision about that until you know whether Scotland is going to remain part of the UK. How can you make a decision about how much devolution when you don't know whether Scotland is going to remain in the UK - is that logical?"
Another amendment to the Scotland Bill will attempt to stop Scottish universities charging students from the rest of the UK up to Â£9,000 a year to study in Scotland, while  other EU students pay nothing.
A number of peers have said the present  system is ''discriminatory" and their amendment calls for an end to the practice.
Although peers are debating the bill on Thursday, the proposals will not be considered until after the UK government's consultation exercise has concluded.

NSPCC Cymru said just two children were reported to North Wales Police in 2013, rising to four in 2014 then 28 in 2015.
Most of those reported - 24 - were aged 15 or under while 10 were 16 or 17.
Des Mannion, head of service at NSPCC Cymru said: "It is very worrying that more children are sharing explicit images of themselves."
He added: "Although the figures in north Wales are relatively small, the fact that there has been a sharp increase in the number of cases reported to police is a concern."
The NSPCC wants children to be warned about the dangers of sexting through compulsory online safety lessons and wants to see the next Welsh Government implement a plan for this.
While the majority of these types of images were shared via mobile phones, they were also sent using apps such as Snapchat, Instagram and Facebook.
Mr Mannion added: "We are very concerned that children are putting themselves at risk of exploitation or bullying in this way.
"Children need to be taught about the dangers of sexting and how the consequences can be devastating if they lose control of an image."
In February, police in England and Wales began producing new guidelines designed to avoid "criminalising" children caught sending indecent images to each other.

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A former Scotland Office minister is calling for a "double referendum" to determine Scotland's constitutional future.
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A rise in under-18s being reported to the police for distributing indecent images of children has raised concerns over 'sexting'.
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An ex-England captain, a former Lance Bombardier in the Army and the most expensive signing in Championship history.