In a news release Friday, Mylan said that it hasn't received an offer and described the idea that Teva might want to buy it as a rumour.
The Dutch company said anti-trust regulators probably wouldn't approve a deal between Mylan and Teva because their businesses overlap in major ways. It said it would thoroughly examine an offer if it received one.
Teva did not immediately respond to a request for comment.
Shares of Mylan NV rose $2.98, or 4.5 per cent, to $69.82. Earlier they spiked up as much as 8.7 per cent. Teva Pharmaceutical Industries Ltd. shares gained $1.42, or 2.2 per cent, to $64.91.
Earlier this month Mylan offered to buy generic drug and ingredients maker Perrigo for about $29 billion, or $205 per share. Perrigo, which is based in Ireland, said it would review Mylan's offer. Mylan says the companies would have had $15.3 billion in combined revenue in 2015.
Teva has about $20 billion in annual revenue, and its executives have spoken recently about their interest in making new acquisitions and consolidating some of the largest companies in the generic drug industry.
"We are ready to take on a transaction," said Sigurdur Olafsson, the head of Teva's generics business, at a health care conference in March.
In a research note written earlier this month, Barclays analyst Douglas Tsao said Teva believes that some of the largest generic drug companies should combine their businesses because they could save a lot of money by merging their manufacturing operations. He said an acquisition of Mylan would "re-establish Teva as the dominant market leader."
Teva gets almost half its revenue from generic drugs. It also makes treatments for central nervous system disorders, respiratory illnesses, and cancer as well as over-the-counter medicines. Its biggest-selling product is the multiple sclerosis drug Copaxone. In March it agreed to buy Auspex Pharmaceuticals Inc., which is developing central nervous system disorder treatments, for $3.2 billion.
Mylan shares are up 17 per cent since April 7, the day before it went public with its offer for Perrigo, and are near an all-time high.