The Sunday Times today reports that Ian Blackford, the SNP Westminster leader, will tell his colleagues to "engage more closely with local voters to better understand fears about independence and boost the chance of a successful yes vote".
The party also reportedly plans to have its MPs spend more time "engaging with institutions overseas", in a bid to derail any potential problems with European countries, especially Spain, if Scotland were to vote yes in any second referendum.
The moves come as the SNP steps up its campaign to convince Boris Johnson to grant a Section 30 Order for a second vote, claiming that the result of the General Election which saw it return 47 MPs to Westminster, was a mandate for a referendum. The most recent Panelbase poll put the support for independence at 47 per cent.
However the Prime Minister has said he will not agree to the holding of a re-run of the 2014 referendum, which saw Scotland vote to remain in the UK.
According to the report, Mr Blackford aims to introduce a rota to allow MPs to get out of the "Westminster bubble" to "win hearts and minds on independence".
A party source said: "The idea is still to take our Westminster responsbilities seriously, but we also want to to do more building that conversation about what the new Scotland should look like - in constituencies and in conversation with civic Scotland and internationally with bodies like the EU and other countries as we build the case for Scotland to be an independent country and extend the hand of friendship."
Scottish Conservative MSP Annie Wells, welcomed the idea as "the SNP will be on doorsteps to hear from the majority of Scots who don't want another divisive independence." She added: "Scots Tory MPs will get far more done than Ian Blackford's part-time politicians who will spend most of their time obsessing over getting indyref2 at all costs."
The SNP has been contacted for comment.