A statement issued by Jefferson Smurfit to the Dublin, New York and London stock exchanges had only confirmed that it had been approached by an unnamed company, but added that discussions were at a preliminary stage.
Shares in the Irish packaging group jumped 15% on the news to 191p, and were at 198p as PrintWeek went to press.
A spokesman for Madison Dearborn said: "As a matter of principle the company does not comment on any transactions we are or are not pursuing."
The offer is believed not to include Jefferson Smurfits 29.4% stake in its US associate, Smurfit Stone Corporation.
Madison Dearborn Partners is one of the largest financial investors in paper and packaging.
The company already owns five paper and packaging businesses, which include recycled containerboard company Bay Street Paper, and Buckeye Cellulose, a producer of speciality cotton pulp and dissolving wood pulps.
It also owns PaperExchange.com, the online paper-trading portal, which still operates in the US but shut its European operations last year.
Christian Georges, an analyst in the paper sector with Crdit Lyonnais Securities Europe, said the Smurfit family, led by the companys chairman Michael, had "always known how to smell danger in terms of business".
"The containerboard industry should take it as a severe warning about the industrys state if the Smurfits are considering selling," he said.
Story by Andy Scott
Have your say in the Printweek Poll
Related stories
Latest comments
"Been there too!"
"Very True"
"Customers expect quality as a basic requirement so quality is no longer a selling point as its a given. Similarly so, accreditations are a nice to have and show customers that you are committed but as..."
Up next...

50 accredited partners offering GGS loans
Guaranteed Growth Scheme receives extra £500m as tariffs bite

Flatter and streamlined organisation
Stora Enso restructure to reflect renewable packaging importance

Took over in the role on 1 April
Paul Brough becomes Mail Users’ Association chair

Birmingham's Marco Pierre White restaurant