Apple Inc. held talks with Intel Corp. about acquiring parts of its smartphone-modem chip business, according to people familiar with the matter, a potential multibillion-dollar deal that would accelerate the iPhone maker’s efforts to develop wireless technology for its devices.

The talks started around last summer and continued for months before halting recently, around the time Apple reached a multiyear supply agreement for modems from Intel rival Qualcomm Inc., some of the people said.

Intel is now exploring strategic alternatives for its modem chip business, including a possible sale—to Apple or another acquirer, the people said. It has already received expressions of interest from a number of parties and has hired Goldman Sachs Group Inc. to manage the process, which is in an early stage. Should there be a deal, it could yield as much as a few billion dollars for Intel, some of the people said.

The Intel-Apple talks, which haven’t been previously reported, reflect growing openness by the iPhone maker toward the idea of big acquisitions, people familiar with the company’s operations said. The talks also are part of broader tumult in the smartphone sector as sales growth has stalled, squeezing the iPhone business that has long driven Apple’s profits.

Apple’s supply deal with Qualcomm—previously the sole supplier of iPhone modems—was part of the resolution of a two-year legal fight over Qualcomm’s royalties for wireless technology. Intel had gained the iPhone business as that feud worsened, then announced after the settlement that it was abandoning development of modems for 5G smartphones.