Compagnie de Saint-Gobain said it will decide whether to accept the offer after the Works Council has been consulted and has given its opinion.
Ardagh said the deal would increase the size of their glass business globally by almost 60%.
The transaction is subject to US regulatory approval and is expected to close later this year.
VNA, which has its headquarters in Muncie, Indiana, is the second largest glass container manufacturer in the US, serving the North American wine, food and beverage industries
It produces nine billion containers annually from its 13 facilities located in the US and employs 4,400 people. VNA has annual revenues of $1.6bn (€1.2bn).
Pierre-André de Chalendar, chairman and CEO of Compagnie de Saint-Gobain, said the offer is a new milestone in the firm refocusing on the habitat sector.
“If the deal is completed, the sale proceeds will be used mainly to strengthen the group's balance sheet, while pursuing its acquisition policy focused on small or medium-sized targets.
“At the same time, Verallia's positions in Western and Eastern Europe, which were recently strengthened by a very promising operation in Algeria, together with its positions in growing Latin American markets, make it a global leader in its markets, with considerable cash generation and development potential."
Paul Coulson, Ardagh Group Chairman, said: “The acquisition of Verallia North America would be another important milestone in the evolution of Ardagh as it would add scale, diversity and value to our global packaging operations.
“It would result in approximately 40% of Ardagh Group’s total sales and EBITDA [earnings before interest, taxation, depreciation and amortisation] being generated in the US.”
Niall Wall, Ardagh Group CEO, added: “It represents an excellent opportunity to provide our US customers with enhanced competitiveness and improved levels of service through the achievement of greater operational efficiencies.”
Ardagh also announced that it will raise, partly in euro and partly in US dollars, a total of $1.45bn equivalent of debt financing through the issue of Senior Secured Notes and Senior Notes.
The proceeds from the issuance and sale of the notes would be used to pay the cash consideration for the acquisition and certain costs.
The deal could build on the acquisition of Anchor Glass in August last year, with Ardagh saying at the time that the $880m deal would increase the size of their glass business by 50% and result in a US glass industry market share of 23%.
Anchor was the third largest glass container manufacturer in the US, producing 5.6 billion containers annually from its eight facilities.