The issue will be debated by rank and file officers at the Scottish Police Federation's annual conference on Tuesday, according to the newspaper.
The Sunday Herald claims to uncover what it describes as "potentially lethal flaws" in Holyrood security in the wake of the Westminster attack.
It says concerns focus on the car park under the Scottish Parliament, which could be vulnerable to a car bomb, and the personal security of the first minister.
The Scottish Sun leads with news that former Girls Aloud pop star Cheryl has given birth to a baby boy.
Meanwhile the Scottish Mail on Sunday reports that an air ambulance regularly piloted by Prince William came within half a second of "catastrophic" mid air collision with a drone. He was not in the helicopter at the time.
And the Sunday Mail reports that a secret police operation has thwarted at least six new gun attacks in a violent gang war. It follows a series of tit-for-tat shootings across Glasgow.
The Sunday Post reports that calls are being made to routinely arm police officers in Scotland, following the terror attacks in London.