They are unhappy at the E4.00 per share price they have been offered and claim that the Ardagh board has not provided sufficient information for them to judge if it is fair.
Caona is a special purpose company controlled by a number of Ardagh's large shareholders. The biggest stakes are held by businessman Paul Coulson and his investment company Yeoman.
Members of the management of Ardagh and some of the directors also have shares in Caona, which claims to have received acceptances for its offer from shareholders holding in excess of 96pc of the company.
John Collins of Donal Reilly & Collins said the firm had been instructed "to investigate if we can bring minority protection proceedings against the directors. Any such action is predicated on establishing that the true value of the shares is greater than the amount offered by Caona".
He said his firm represented in excess of 2 per cent of Ardagh's approximately 700 shareholders.
Ardagh Glass was spun off from Ardagh (since renamed South Wharf) in 2003 and taken private at a valuation of E1.10 per share.