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
"Brilliant News. A perfect fit."
"So the Ricoh can now do what Xante and Oki have been doing for years?"
"Yes indeed Neil, I was undertaking a project for Pindar ( back in the day 😉 ) and it needed to go to Monarch for indexing so I popped in to ensure we supplied it as required and they were both very..."
Up next...
Operational improvements
Tracked deliveries and parcels boost Royal Mail performance
More than 33,000 sites
Bauer Media expands reach with OOH buy
£1.4m investment backs up major press purchases
Wilkins sharpens up cutting capacity with another Bobst Expertcut
'Where Visionaries Meet'