Earlier this month, Mylan offered to buy Perrigo for $205 per share in cash and stock. Perrigo said Tuesday that previous offer substantially undervalues the company.
A new bid from Mylan will include firm financing commitments, and firm commitments to move ahead with a deal, sources said.
Following CNBC's first reporting of that new development in Mylan's plans, Perrigo's stock rose from 1.5 percent up on the day to about a 3 percent gain from the open.
Mylan's stock, meanwhile, went from slightly up on the day, to a slight loss, following CNBC's report.
Earlier Tuesday, Reuters reported that Perrigo was set to reject the $29 billion offer from Mylan, as it tackles an unsolicited offer from Israeli drugmaker Teva Pharmaceutical.
Perrigo, which has 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.
for the latest on the markets.
—Reuters and CNBC's David Faber contributed to this report.