The government and Bank of Estonia (EP) are looking for ways to remove 1 and 2 cent coins from circulation as they are rarely used and have a large environmental footprint.
Every year, EP produces 50 tons of 1 and 2 cent euro coins but they rarely end up back in circulation as they are cumbersome to carry around.
The production costs and environmental impact are disproportionately large compared to their value, the bank said in a statement on Monday.
EP and the Ministry of Finance are now seeing feedback from interest groups.
Under the draft plan, the coins could still be used to buy items in-store but could not be returned as change.
It is also proposed to round up the final bill at grocery stores to the nearest 5 cents when shoppers pay in cash. Individual goods would not all rise in price.
For example, if a single item costs 28 cents, it would cost 30 cents at the till. But if two items totaled 56 cents, the customer would pay 55 cents.
EP believes rounding up or down would have little effect on prices and the situation would not change for those who pay by card.
Many countries across the EU face similar problems. Finland, Ireland, the Netherlands, Belgium, Slovakia, and Italy already round up prices. Lithuania is also planning to do so.
Editor: Helen Wright