Clinton aides have spoken of the earlier timetable in private meetings, according to people engaged in recent discussions about the presumed Democratic front-runner’s emerging 2016 campaign. Many within her camp have advocated her staying out of the fray until the summer.

Jumping in sooner would help the Democratic field take shape, reassuring party leaders and donors that the former first lady, senator and secretary of state is running. A super PAC loyal to Mrs. Clinton has faced hesitation from donors who don’t want to make...