The UK arm of the American company, which is controlled by private equity firm Alcuin Capital, is planning to float on the London Stock Exchange next month.
The float, which will value the firm at around £200m, is being handled by Investec, which will send marketing materials to City fund managers this week, the Sunday Telegraph first reported.
Krispy Kreme’s planned float is one of a number being lined up for the London Stock Exchange currently.
Technology company Misys is plotting a £5.5bn float, which would be London’s largest of 2016, while mobile network O2 has also said it could launch an IPO as soon as this year.
Krispy Kreme was founded in North Carolina in 1937 and opened its first UK store in 2003 in Harrods. It has since opened stores across the UK, including in Edinburgh, Bristol, Birmingham and Leeds.