Mylan shares were up 14 percent on Wednesday. It said the potential deal could help drive synergies and expand operating margins.
Mylan's proposal comes on the heels of a flurry of biotechnology and pharmaceutical merger activity last week, including drugmaker Teva's announcement that it would buy Auspex for $101 per share.
Read MoreTeva to buy Auspex in all-cash deal
Perrigo, with a large and attractive portfolio of over-the-counter consumer products, infant formulas and a line of generic topical pharmaceutical medicines, has long been seen as a takeover target. Mylan has been at the center of deal speculation as one of its main rivals, Actavis, has swallowed upcompanies to expand beyond generic medicines, including a deal tobuy Botox maker Allergan.
— CNBC's Meg Tirrell and Reuters contributed to this report