The union can only remain workable if "maximum devolution" is handed to Scotland, according to a senior Labour MEP.
David Martin said there is growing support within his party for another new constitutional settlement in the wake of the Brexit vote.
He said more powers beyond those given to Holyrood following the independence referendum are now required because of a further fracturing of the relationship between Scotland and England.
He made the remarks as he gave evidence to the Scottish Parliament's European and External Relations Committee.
Senior party figures including Scottish Labour's deputy leader Alex Rowley, former prime minister Gordon Brown and ex-first minister Henry McLeish have already advocated a move towards a federalised UK.
Mr Martin told the committee: "My own view is that whatever happens post-Brexit, the relationship between Scotland and England has been fractured further than it already was."
He added: "If you want to keep it (the union) workable, maximum devolution is now the only option. Scotland has clearly indicated that it has a different set of preferences to... England.
"Yet again we need to be looking at another constitutional settlement, and among that, I think labour and employment are a key element."
Asked if he could convince his party colleagues, he added: "Actually I think you would be surprised that there is a growing movement inside the Labour Party as well that recognises that there is a need for a new relationship, but not everybody agrees with that of course."
Mr Martin also warned that a "hard Brexit", where the UK would not retain single market membership, would make Scottish independence more difficult to achieve.
First Minister Nicola Sturgeon has said the option of a second referendum on leaving the UK remains on the table ahead of any EU negotiations.
"On the narrow issue of jobs, a hard Brexit means the UK is out of the single market, and if the purpose of independence is to keep Scotland in the single market, then we would face... a hard border between Scotland and England," Mr Martin said.
"A hard border in that situation would not be good news."
He also warned the defence of Scottish interests in Europe should be handled "delicately".
He added: "If defending the Scottish interest is seen as promoting independence, you will find some hostility in the (European) Parliament."
SNP MEP Alyn Smith, also appearing before the committee, agreed: "If there is a perception that we are using this as a pretext for a mad dash for independence, there will be a backlash."
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