US Airways Group Inc. CEO Doug Parker, after three failed attempts at major mergers, is approaching a deal to combine with AMR Corp.’s American Airlines and form the world’s biggest carrier.

Parker, 51, has applied lessons from his previous efforts, shifting tactics in pursuing the bankrupt AMR. The two companies are working on final details and their boards may vote on the deal later this week, people familiar with the matter have said. Parker would lead the combined company, the people said.