Broadcom had offered $70 per outstanding share for a total value of $130 billion.
Broadcom has also been deliberating the possibility of raising its bid for Qualcomm, including through more debt financing, some of the sources said, although it was not clear when Broadcom would choose to make such a move.
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"After a comprehensive review, conducted in consultation with our financial and legal advisors, the Board has concluded that Broadcom's proposal dramatically undervalues Qualcomm and comes with significant regulatory uncertainty", Qualcomm's Presiding Director Tom Horton said in a statement.
If completed at the current price, the combined companies would have had annual sales of $51 billion - trailing only Intel and Samsung in the semiconductor industry. It is engaged in a patent infringement dispute with Apple Inc (AAPL.O), and is also trying to close its $38 billion acquisition of automotive chipmaker NXP Semiconductors NV (NXPI.O) after signing a deal in October 2016. CEO Hock Tan last week, saying the company is likely to relocate its headquarters from Singapore to the United States.
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Qualcomm stock, which rallied on the report of the offer, has traded below the bid price on skepticism that a transaction can be completed.
Overall, Broadcom's bid is a very ambitious attempt to grow its share of the market for components that go into mobile phones.
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On Monday, Qualcomm said in a press release that the San Diego, Calif. -based company's Board of Directors has unanimously rejected the proposed deal. The company did away with the provision in 2015 during negotiations with Jana Partners.