According to news reports the group beat off rival bids from companies including Norway's Exopac to increase its hold in SIG, which is one of the worlds leading suppliers of beverage packaging solutions.
The decision continues Rank's plan to expand its presence into the lucrative US and European packaging markets, increasing competitiveness amongst its regional rivals to meet demand for food packaging.
SIG revealed in a statement that Rank now holds a 22 per cent stake in its operations and are keen to increase its holding within the company.
Under the new pricing of €271 a share, SIG could be acquired for about €1.7bn.
Phillip Hart, the owner of Rank had previously failed to acquire the company with a €1.5bn bid for SIG that was turned down.
If the revised bid is successful, the merger would see Rank become the world's second largest producer of beverage packaging, after Tetra Laval.
SIG had sales of €1.2bn last year from products such as cartons for long life drinks and polyethylene terephthalate (PET) bottles.
The purchase would add to Rank's considerable holdings in the global packaging industry, a portfolio that the investment company has been building for the past year.
Last month, Hart finalised a deal to acquire International Paper's drinks packaging business for €382.8m.
This has allowed Rank to sell products such as liquid paperboard packaging for dairy products and juice. The unit has plants in North America and Asia.
The sale highlights the growing appetite amongst Asia Pacific companies to enter into the dynamic US and European beverage packaging industry.
Last year, Australian firm Amcor revealed that it had managed to offset declining revenues from its cardboard operations through increased sales of its beverage products in the US and Europe.
This saw the group - which is already the world's largest producer of plastic bottles - increase its sales throughout the sector.
Of this increase, aluminium beverage cans proved a particularly strong segment with sales rising 6 per cent, though the company also reported strong sales of glass wine bottles which also performed well.
