The Deputy Prime Minister said the First Minister's involvement would ensure further devolution happened quickly and "on the most ambitious scale possible".
Mr Clegg insisted there was "unstoppable momentum" behind further devolution. His comments echoed Prime Minister David Cameron, who last week sought to reassure Scots that Holyrood would be handed more powers in the event of a No vote.
The SNP again dismissed the promise, saying independence was the only way to guarantee further devolution.
Mr Clegg was speaking after addressing business leaders in Edinburgh.
He said, in the event of a No vote, he hoped the SNP would not "take their bat and ball away" and would discuss possible constitutional changes with the other parties.
He said: "Clearly the SNP will have to overcome the disappointment of not securing their cherished goal of pulling Scotland out of the UK.
"I hope they would be able to overcome that disappointment and play a role.
"The more we can secure a broad-based consensus in favour of further devolution the more likely it is going to happen both quickly and on the most ambitious scale possible."
His comments follow Mr Salmond's proposal for a broad negotiating team to shape Scotland's future in the event of a Yes vote.
The First Minister has said representatives from other parties and civic Scotland would be invited to join what he has called "Team Scotland" to negotiate with the UK on issues such as sharing assets and dividing the national debt.
However, Mr Clegg's idea of building cross-party consensus around a new devolution package is not shared by Labour or the Conservatives. They are likely to press ahead with their own proposals if they win a mandate for them in next year's Westminster election.
In his speech to the Scottish Chambers of Commerce, he said: "The SNP are unwilling to admit the nature of this debate has fundamentally changed.
"Further powers for Scotland have been delivered in this Parliament and, if Scotland remains in the UK, they will be delivered in the next.
"The SNP are pouring scorn over the proposals I and others are making for further devolution but by doing so they are living in the past.
"We'd like them to be part of the changing conversation over Scotland's future, not just repeating grievances from the past."
Answering questions from business leaders later he added: "I really do think we have the makings of an unstoppable momentum that will make further devolution inevitable."
The Liberal Democrats have backed proposals for a wide- ranging package of powers, including handing Holyrood full control over income tax, capital gains tax and inheritance tax in Scotland.
The Scottish Parliament would not be able to set the rate of corporation tax, under LibDems' plans, but would receive the money raised from it in Scotland.
Labour's plans include giving MSPs greater - but not full - control over income tax. The tax will be partially devolved from 2016.
The Scottish Conservatives are also expected to back further devolution of income tax when they unveil constitutional proposals later this month.
Mr Clegg also used his speech to attack the SNP ahead of Thursday's European elections. He likened Alex Salmond's party to Ukip, claiming both were putting Scotland's membership of the EU at risk.
According to polls the SNP are on course to claim the LibDems' only European seat in Scotland.
SNP MSP Annabelle Ewing said: "Given that Mr Clegg's party have been promising Home Rule for over a hundred years, people in Scotland are unlikely to view them as the guarantors of anything - except continued Tory rule from Westminster."
She added: "The LibDems are paying the electoral price for abandoning their principles and going into coalition with the Tories."