Pirelli now plans to price its shares at between 6.5 and 6.7 euros each, compared with initial guidance of between 6.3 and 8.30 euros a share.
The IPO, in which Pirelli is offering up to 40 percent of its capital, is fully covered within the tightened price range and books are expected to close on Thursday at 1200 GMT, the memo showed. The final price is expected on Friday.
In the new narrowed range, Pirelli is set to raise up to 2.68 billion euros through the IPO, including the additional greenshoe option.
Established in 1872 and one of Italy's best-known corporate names, Pirelli is expected to return to the Milan stock exchange on Oct. 4.
The world's fifth-largest tyremaker had traded on the same exchange since 1922 before it was de-listed in 2015 following a takeover by China National Chemical Corp (ChemChina).
State-owned ChemChina took over Pirelli two years ago by acquiring a 65 percent stake in the holding company controlling the maker of tyres for Formula One motor racing teams and upmarket brands such as Mercedes, Audi and BMW.
The relisting will test demand for a streamlined firm that focuses on high-end consumer tyres after its less profitable truck and industrial tyre business was folded into a unit of ChemChina.
The initial price range was already a little lower than core investors had hoped.
Pirelli is more profitable than many rivals, including France's Michelin (>> Michelin) and Germany's Continental (>> Continental), but its core profit (EBITDA) margin of around 20 percent lags that of market leader Nokian (>> Nokian Renkaat Oyj), which stands at nearly 30 percent.
Through its focus on more high-end tyres, Pirelli has become less cyclical than in the past. With upmarket tyres expected to account for about 63 percent of revenue by the end of 2020, Pirelli aims to market itself as a top-end industrial player.
But others, such as South Korea's Hankook (>> Hankook Tire Co Ltd), have followed suit and may affect market share and pricing in the premium tyre market, analysts have said.
Pirelli's targeted average revenue growth of at least 9 percent per year between 2016 and 2020 is doable but ambitious, analysts have said. But some have raised concern about its heavy debt load as well as management succession, with long-standing CEO Marco Tronchetti Provera set to retire after 2020.
A question mark also remains over the role the Chinese will play at the company after the IPO, although the tyremaker has repeatedly said ChemChina - which is set to reduce its stake to below 50 percent through the IPO - would continue to have a hands-off attitude to the company's management.
(Writing by Agnieszka Flak; Editing by Keith Weir and Mark Potter)
By Elisa Anzolin