Place currants, sugar, and 2 tablespoons water in a medium saucepan over medium heat; stir to combine. Bring to a boil, reduce heat to a simmer, and cook, stirring occasionally, until soft, about 15 minutes.
Strain mixture through a fine mesh sieve set over a medium bowl, pressing on solids with a spatula or the back of a wooden spoon to extract liquid. Discard solids and chill liquid before using. Red currant puree can be refrigerated in an airtight container for up to 7 days.