Creating frustration for his inner circle, as Mr. Cuomo considers a 2016 campaign for the White House, the eyes of his party are fixed on Mrs. Clinton, whose already sky-high stature among Democratic activists was enhanced by her husband’s crowd-pleasing speech this month at the party’s convention in Charlotte, N.C., and who can count on broad support if she decides to run.

Mrs. Clinton complicates Mr. Cuomo’s ambitions in several ways. Despite the fact that she hails from Illinois, she is now viewed as a New Yorker and commands deep loyalty from the state’s Democratic establishment. And Mr. Cuomo, 54, reveres her husband, former President Bill Clinton; he views Mr. Clinton as a mentor who helped him begin a career in politics, according to Cuomo friends and associates…

What is most vexing to those who want to see Mr. Cuomo run is that Mrs. Clinton, given her popularity in the party, can take her time deciding whether to make another bid for the presidency, essentially freezing the rest of the Democratic field.

Mr. Cuomo, in private conversations, has often been frank about his own prospective presidential candidacy. “First, I’ve got to figure out what Hillary is doing,” he says, according to an adviser.