Analog approached Maxim, which was working on a strategic review, about a possible combination, Bloomberg reported, citing sources. The outlet said talks are ongoing and a deal may not be imminent.
Both stocks jumped as much as 12 percent Wednesday. Analog and Maxim had market values of about $18 billion and $10 billion, respectively, before the news.
The companies would seek scale in the semiconductor industry, which has grown increasingly consolidated. Merger and acquisition deals in the segment already top $100 billion this year.
Massachusetts-based Analog makes signal converters and amplifiers. Maxim, based in California, sells most of its chips for consumer devices.
Both companies told CNBC they did not comment on rumors and speculation.