WASHINGTON  Democratic leaders in the Senate are prepared to give Senator Hillary Rodham Clinton a still-undefined leadership role there if she does not become Barack Obama’s secretary of state, Democratic officials close to the situation said Thursday.

The discussions about an enhanced position for Mrs. Clinton are factoring into her deliberations over joining the cabinet, the officials said. Mrs. Clinton, the junior senator from New York, is wrestling with whether to abandon her independence to become the nation’s top diplomat or remain in a chamber where lack of seniority limits her influence.

Mrs. Clinton asked to join the Senate Democratic leadership after the Nov. 4 election, and party leaders began trying to figure out a way to accommodate her without dislodging any of the current leaders, Democratic officials said. The conversations, they added, preceded Mr. Obama’s approach to her about becoming secretary of state and are on the table if she turns the job down.

Although advisers to Mr. Obama have said he has not made a formal offer, most Democrats believe the decision is hers to make, and friends said Thursday that she was wavering.