The news comes after the Scottish Government published its draft bill on a second referendum, which have gone out to a public consultation.
First Minister Nicola Sturgeon, pictured above left, has called for a vote to be held before the United Kingdom leaves the European Union, but Prime Minister Theresa May has denied there is a mandate for a referendum to be held.
In September 2014, 55pc of Scots voted to remain as part of the UK.
Jo Robinson, who edits the two papers, said: “We’re always looking to engage with our readers to find out what they think.
“Independence is such a hot topic it seemed like an obvious one to survey – both for the Border Telegraph and its sister paper the Peeblesshire News.
“As ever, our readers haven’t disappointed, so I’m sure there will be plenty of lively debate to report in this week’s papers.”