The group, which has five of its 310 outlets in Edinburgh, is expected to have an enterprise value of between 800 million-900m.
Such a price would mark a huge return for TDR and Capricorn Ventures, the two private equity groups who took a massive gamble and bought the chain in 2003 for just 280m under parent company Gondola Holdings.
Gondola, which operates the Pizza Express estate as well as Ask and Zizzi restaurant chains, said that David Ross, the co-founder of mobile phone retailer Carphone Warehouse would be the group's chairman.
Mr Ross said: "We see significant opportunities for further roll-out of our brands. We look forward with confidence to our future as a UK publicly-quoted company."
Gondola, which has about 500 restaurants in total and employs about 10,000 staff, said the planned stock market debut will raise cash to pay off its debt and will see the firm step up its expansion with the opening of up to 30 new outlets each year.
A number of staff, including restaurant managers, are expected to be given shares in the company, although it is not yet known how much they will receive.
Nigel Popham, an analyst at Teather and Greenwood, said: "Those companies with good brands and value for money will continue to grow market share."
In a trading update, Gondola added: "Certain of the group's central London restaurants experienced short-term trading disruptions in late July and August of 2005 following the bombings in London," Gondola said in a statement.
"Since the beginning of September, trading across the estate has continued to show good growth with trading in central London restaurants improving."
And since then, same-store sales across the group increased by 3.2 per cent in the 16 weeks to October 16, compared with the same period last year.
Pizza Express was taken private for 278m just two years ago by investment firms TDR Capital and Capricorn Ventures, who later bought Ask and Zizzi.
The brand can trace its roots back to 1948 when founder Peter Boizot tasted his first pizza in Florence and decided to recreate the experience in London.
Pizza Express quit the stock market in May 2003 after founder Luke Johnson failed in a power struggle to gain control of the firm, which was seeing sales slide and which at the time had an uncertain long-term future.
The company began to feel the bite of the tourism downturn in 2002, which followed on from the September 2001 attacks on America and trade began to drop off. That forced analysts to make a string of downgrades of their expectations for the firm.