Broadcom, which specializes in broadband communication, is valued at $28 billion. Shares of Broadcom have risen about 76 percent over the last 12 months.
Avago provides services and makes products for four major markets, including wireless communications and enterprise storage, according to the company's website. Avago's shares rose more than 7 percent to $140 in afternoon trading on the news.
Avago's stock was trading at all-time highs back to its IPO in August 2009 while Broadcom's stock was having its best day since January 2006.
The report said the terms and timing the companies were discussing for a potential deal were not clear. The two companies could not immediately be reached for comment.
A person familiar with the matter confirmed that Avago's board will meet Wednesday evening to vote on the deal, which could be confirmed as early as Thursday morning. The company is set to release its second-quarter earnings on Thursday, as well.
—Reuters and CNBC's Kayla Tausche contributed to this story.