The three - two based in Fife and one from East Dunbartonshire - all scooped £1 million in the EuroMillions Millionaire Raffle draws in July.
But they have not yet come forward to collect their life-changing winnings and the 180-day period in which they can do so has almost expired.
National Lottery bosses are urging EuroMillions players in those areas to look for their old tickets and not to “run away” from their windfalls.
For every EuroMillions line played, UK players automatically receive a EuroMillions Millionaire Raffle selection printed on their ticket.
Two of the winning tickets, one from Fife and one from East Dunbartonshire, are from the draw on July 26. The winning raffle numbers are CZZ474287 and CBT475280. The deadline by which the winners can claim their winnings is 11pm on Wednesday January 22.
The other winner from Fife netted £1 million in the draw on July 23 with the raffle number BZP849967. They only have until 11pm this coming Sunday, January 19, to claim the prize.
A National Lottery spokesman said: “There are three lucky winners in Scotland walking around not knowing they are millionaires.
“Though the clock is ticking, there is still time for players to re-check their tickets and, for a lucky trio, to make 2014 a year to remember as Scotland’s newest millionaires.
“We urge EuroMillions players to check their bags, coat pockets, even down the back of the sofa and in their cupboards - the winning tickets could be tucked away in any of these places.
“EuroMillions Millionaire Raffle is life-changing and we are desperate to give our three missing millionaires in Scotland one last chance to race into the New Year as a millionaire.”
Anyone who believes they have a winning ticket for any of the National Lottery draws within the 180-day deadline should call the National Lottery Line on 0845 910 0000.
If no-one comes forward with the winning tickets before the deadlines, then the prize money and all the interest it has generated will go to the National Lottery Good Causes fund.