Gordon Wilson said the revival of the Yes Scotland campaign group would enable the party to build a stronger support base for any future vote, and put pressure on the Scottish Government.
Yes Scotland lost the 2014 independence referendum, after 55 per cent of Scots opted to stay in the UK.
First Minister Nicola Sturgeon has said a second vote on the constitutional question is “highly likely” after Scotland voted to stay in the EU, while the UK as a whole voted to leave.
While she is considering all options to protect Scotland’s place in Europe, she said on Sunday she will consider calling a second independence referendum if the UK Government triggers formal Brexit negotiations without a satisfactory UK-wide approach being established.
Brexit Secretary David Davis has suggested Article 50 - which fires the starting gun on the two-year negotiating period to leave the EU - would be triggered “early next year”.
Ms Sturgeon has instructed Scottish Government officials to draft legislation for Holyrood in preparation for a second vote, while the SNP is to undertake a new drive for independence this summer.
Mr Wilson, who led the party from 1979 to 1990, said: “Unlike 2014, Indyref2 must have a stronger readiness base to encourage the people to support independence.
“It is no secret that I am sceptical of the chances of victory in a premature second attempt. But the position is incredibly dynamic.
“Support for independence in the aftermath of the EU Referendum has risen to 55 per cent with many former unionists switching to independence to safeguard our country’s position in the European Union.
“While still not at the critical level of 60 per cent that would guarantee victory, independence could be within reach.”
He added: “I call upon the SNP to consult with the Yes groups that performed so well in 2014 with a view to reviving a Yes Scotland campaigning organisation to mastermind the steps to bring support for independence up to 60 per cent and to coerce the new London Government to concede a fresh independence referendum as a last resort should the negotiations to deliver access to the European single market break down.
“The formation of Yes Scotland will remove a large part of the burden from the SNP Government and permit it to concentrate on the negotiations.
“It will also demonstrate to London that a second referendum is on the cards if it proves obdurate and puts barriers in the way of Scotland securing access to the single market.”
An SNP spokesperson said: “There is no doubt that many people who voted against independence in 2014 - based on assurances from the No campaign that it was the only way to protect Scotland’s EU status - are now reconsidering their position.
“The SNP Government is currently exploring every possible option to protect Scotland’s EU relationship - but if it becomes clear that the only way to do that is by becoming an independent member, then that option must be on the table.
“That is why the necessary legislation is being prepared to enable a referendum to take place if and when Parliament so decides.”