Bounties should be paid for the shooting or trapping of grey squirrels, according to a Conservative MSP.
The MSP said bounties would offer an incentive to cut numbers
Murdo Fraser said consideration must be given to such measures to preserve numbers of native red squirrels.
The party's deputy leader said that only suitably qualified people with shotgun licences, like gamekeepers, would get the money.
However, an animal protection group said the proposal would lead to "carnage in the countryside".
Scotland is reported to be home to more than 75% of the UK's red squirrel population. However, they have been under threat of being displaced by the non-native grey.
Grey squirrels compete for food with the red squirrels and can carry a virus which kills them.
Should grey squirrels be culled to preserve red numbers?
Results are indicative and may not reflect public opinion
Scottish Natural Heritage has announced plans for a cull in areas including the north east, Argyll, Loch Lomond and the Highlands, where reds are most under threat; and grey squirrels are being shot on sight by patrols in the Borders.
Bounties have previously been paid in the UK but the system was abandoned in the 1950s because of abuse.
Mid Scotland and Fife MSP Mr Fraser said the smaller population could be wiped out unless action is taken and a bounty of a few pounds per grey should be on offer.
He has lodged a motion in the Scottish Parliament seeking the backing of fellow MSPs for his proposal.
He said: "Scotland's red squirrel is now under serious threat from a foreign invader.
"Areas such as Perthshire and Angus are now the frontline for the red squirrel and we are seeing their numbers under threat in these areas."
On the proposal for bounties, he said: "It may seem like a drastic step, but the seriousness of the current situation cannot be underestimated.
"Paying bounties to gamekeepers and others to eradicate the grey squirrel in areas where they threaten red squirrels would be a positive and imaginative step to try and tackle this serious issue."
Ross Minett, director of Advocates for Animals, said: "This is an absolutely ridiculous idea and it would lead to carnage in the countryside with every man and his dog out to raise cash from the killing of squirrels.
"Mr Fraser obviously hasn't studied ecology because if he had he would realise that the grey squirrel is here to stay and killing them in vast numbers is not going to remove them.
"It would be a complete waste of time and taxpayers' money."