The firm is looking to raise £10m from its Aim listing, City A.M. understands.
It has also secured fashion industry big-hitter Peter Cowgill, chairman of JD Sports, as its non-executive chairman.
Fashion retailers geared towards young women buying clothes online have been booming on the stock exchange.
Last week, Boohoo's shares jumped by 17 per cent in a single day after it revealed a sales boost of 106 per cent, and said it was seeking funding for a new warehouse because it was facing such high demand.
Quiz, which has been valued at a potential £200m, targets the same consumers and today boasted total sales growth of 37 per cent year-on-year in the first two months of the financial year.
Tarak Ramzan, chief executive of Quiz, said: “The group’s fast, flexible supply chain together with the winning formula of style, quality, value and speed-to-market has enabled Quiz to grow rapidly into an established international fashion brand with over 300 standalone stores, concessions, franchise stores, wholesale partners and international online partners in 19 countries."