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The comments came days after Singapore-based Broadcom escalated its efforts on a $130 billion bid by proposing a slate of directors to unseat the Qualcomm board of directors.
Mollenkopf, speaking at an event hosted by The Economic Club of Washington, said that "we always have discussions" on potential tie-ups but that Qualcomm's future is well-positioned as an independent company.
He added that "we didn't think the offer was in the ballpark of value," and that "there is a lot of uncertainty" on whether the merger - which would be the largest ever in the technology sector - could pass regulatory muster.
"There's no real path to value that we see in terms of offers now in terms of an alternative" to remaining independent, he said.
Mollenkopf maintained that Qualcomm, the leading global supplier of smartphone chips, is well-positioned for emerging technologies for connected devices and 5G, or the fifth generation of wireless networks.
"We're probably the best positioned company for 5G and the connected world," he said.
He noted that the company is "in a momentary spot where our revenue is a little difficult to model" because of a series of legal disputes, including with Apple, but predicted that "those will get resolved."
Mollenkopf also said he expects Qualcomm to finalise later the year or early in 2018 a $47 billion acquisition of Dutch rival NXP, a deal that is the subject of a European Union anti-trust probe.
Broadcom's announcement on Monday sets the stage for a fight at the Qualcomm shareholder's meeting in March, by proposing a slate of directors likely to press for the merger or replace management.
If completed the deal would be the largest-ever in the tech sector and create a powerful player in the booming sector fueled by growth in smartphones and an array of connected devices from cars to wearables.
Any merger deal would need to pass muster with Qualcomm shareholders and could face regulatory scrutiny in the United States and other markets.
Broadcom's November 6 proposal followed a visit by its CEO Hock Tan to the White House, where he met President Donald Trump and announced plans to move the tech company back to the United States from Singapore.