Wally Backman, a candidate for the Mets’ managerial opening last offseason, could soon leave the organization, according to a team source.

The fiery Backman, 52, is considering the possibility of joining Davey Johnson’s coaching staff with the Nationals — likely as the third-base coach. The Nationals have not yet officially announced Johnson will return next season, but that is considered a formality.

The source said 68-year-old Johnson may look to groom Backman for the managerial job, much in the same manner Bobby Cox took Fredi Gonzalez under his wing with the Braves before retiring. Johnson was Backman’s manager with the Mets in the 1980s, a run that culminated with a World Series title in 1986.

Backman spent last season managing Double-A Binghamton to a 65-76 record in the Eastern League. He is the front runner to manage at Triple-A Buffalo next season if he stays with the Mets, but he is not a candidate for the major-league staff.

The Mets recently promoted Tim Teufel, who spent last season managing at Buffalo, to third-base coach with the major-league club. Chip Hale, who had been the Mets’ third-base coach, last week was named Athletics bench coach.

The Mets are still searching for a bench coach and first base coach. Ken Oberkfell and Mookie Wilson will not return next season.

Backman was a finalist — along with Hale and Bob Melvin — for the managerial job that went to Terry Collins last winter. The Mets recently picked up Collins’ option for 2013, and Backman could view the Nationals’ coaching opportunity as a quicker path to managing in the big leagues.

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Jim Riggleman is expected to interview for the Mets’ bench coach vacancy tomorrow. As The Post first reported last week, Riggleman and Larry Bowa are among the candidates on Collins’ list for the position.