Online marketplace eBay Inc. and activist investors Elliott Management Corp. and Starboard Value LP are nearing a settlement deal that would give the activists board seats and could open the door to the company breaking itself up.

The three parties are discussing a deal in which Elliott and Starboard would receive multiple board seats, according to people familiar with the matter. The company would also agree to perform an operational review focused on improving profitability and a full-company strategic review—which is expected...