The firm, which has been increasing its presence in the UK in recent years, confirmed that Sheffield was one of its target markets for 2019-20.
The firm's chief executive Frederic Vecchioli said the company had enjoyed a strong year and that it planned to expand even further in the coming years.
He said: “Further to our successful openings this year, we plan to open new stores in London Carshalton, Gateshead, Sheffield and Paris Magenta during the 2019/2020 financial year, adding 175,000 sq ft of further capacity to our estate.”
Safestore was founded in 1998 and acquired the French Une Pièce en Plus' brand six years later, making it the second largest self-storage company in Europe.
It became a publicly traded company on the London Stock Exchange in 2007 and claims to serve around 60,000 customers.
The Hertfordshire firm increased its revenue by £7.9million in the 2018/19 financial year to £151.8million.
It has also announced a £15million deal to enter the Spanish market after acquiring four stores in Barcelona after taking possession of Spanish firm OhMyBox
The group also purchased a 20 per cent stake in Dutch firm M3, which has six stores in Amsterdam and Haarlem.
The firm is the UK’s largest self storage company and currently has 95 outlets across the UK.
The planned openings for this year will push the firm over the 100 mark for the first time.