Shares of Akorn, which has a market value of about $3.7 billion, were up 10 percent at $32.60 in aftermarket trading.
There can be no assurance any transaction will result from these discussions, Fresenius said in a statement.
Akorn confirmed the talks with Fresenius, whose businesses range from kidney dialysis and tube feeding equipment to running hospitals.
Fresenius's chief executive, Stephan Sturm, had signaled that acquisitions would be a hallmark of his leadership after he took over the top job in July.
In September, the company made its biggest deal ever with the acquisition of Spain's private hospital chain Quironsalud for 5.8 billion euros ($6.14 billion), including assumed debt.
Bloomberg had reported earlier in the day that Fresenius was weighing a bid for the company.
($1 = 0.9441 euros)
Reporting by Akankshita Mukhopadhyay in Bengaluru; Editing by Anil D'Silva