West, who is nearly 80, played the Caped Crusader on the action series in the 1960s.
"Adam is in outstanding shape," a source told the New York Post. "He works out an hour a day and walks with his big dog on his farm in Sun Valley, Idaho."
West's publicist confirmed that, while nothing is definite yet, the actor is "one of the people they are seriously looking at" for the next season of the dance competition show.
"They will decide on everyone on Aug. 25," the representative told the Post.
2014: The Year in Fashion [PHOTOS]
Mindy Kaling mistaken for Malala Yousafzai