Depends on your definition.
If you include those elected for something other than playing, then it’s Tommy Lasorda, who is 91. LaSorda did play in MLB briefly, but his playing career played no role in his election to the Hall. His lifetime winning percentage as a pitcher was a nice round zero. Taking second place, just two months younger than Lasorda, is a man from the broadcasters’ wing of the Hall, my fellow Fordham alum (where we both majored in English and announced on WFUV), the legendary Vin Scully. Both Lasorda and Scully earned their greatest plaudits with the same team, the Dodgers.
If you’re talking about those who earned their plaque on the playing field, then the elder statesman is the crafty old lefty himself, the great Whitey Ford, who is 90. Second place in the player wing goes to Willie Mays, who some argue is the greatest overall player ever to grace the diamond. The Say Hey Geezer turns 88 next week.
All four of those men began their careers on teams based in New York. Lasorda and Scully started with the Brooklyn Dodgers, Mays with the New York Giants, Ford with the New York Yankees. Ford and Scully were also born in New York. This is not a demonstration that New Yorkers are long-lived, but rather a reflection of how important New York was to the game before 1958.
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The oldest living major leaguer is somebody you probably never heard of, because I never heard of him before I started typing this paragraph. His name is Tom Jordan, a bench-warmer who retired from MLB before I was born!