General Electric Co. is nearing a deal to sell a unit that makes large industrial engines to private-equity firm Advent International for $3 billion or more, people familiar with the matter said, a move that would bring in needed cash for the struggling conglomerate.

A deal, if completed, could be announced on Monday, the people said. Advent appears to have beaten out Cummins Inc. CMI, +0.91% in an auction for the businesses, according to the people.