Former first minister Alex Salmond and Westminster leader Angus Robertson are among six MPs proposing the change.
The Scotland Bill enters its final parliamentary stage with a House of Commons debate and vote on Monday.
Holyrood decided the timing and some rules for the 2014 referendum but only after temporary powers were granted.
The vote took place after the signing of the Edinburgh Agreement between the UK and Scottish governments which gave the Scottish Parliament the power to hold a single-question referendum until the end of 2014.
Scotland's First Minister Nicola Sturgeon has said a second vote on the issue would only be held when there is "strong and consistent" evidence that the majority of Scots want to leave the UK.
But she also warned that demand for another ballot could be "unstoppable" if Scotland was removed from the EU against its wishes in the forthcoming in/out referendum on membership.
Pete Wishart, one of the six MPs behind the new amendment, told the Sunday Herald newspaper: "It's in response to all the conversations going on about a second referendum, how that could be triggered and who has responsibility.
"This is a power that should rest with the Scottish people and if they decided the moment and the conditions were right, that would be a matter for Scotland and the elected representatives of the Scottish people, not Westminster. That call should be made by Scotland."
Last week the UK government revealed more than 80 amendments it has tabled on the bill, which is designed to implement the post-referendum Smith Commission on devolution.
Senior SNP MPs have tabled an amendment to the Scotland Bill calling for Holyrood to be given control over any future referendum on independence.