Sen. Robert C. Byrd (D-W.Va.) did little yesterday to dampen mounting speculation that he may bow out as majority leader late next year and move on to some other prestigious position in the Senate.

The speculation was fueled by the announcement this week that Sen. John C. Stennis (D-Miss.), chairman of the Appropriations Committee, will not seek reelection next year. With Stennis gone, Byrd, 69, the second-ranking Democrat on the committee, would automatically rise to that influential post.

"I have so many important issues on my mind that I am not ready to devote time to that decision," Byrd said yesterday through an aide. "There are vital matters that we in the Senate must deal with . . . and my personal position is relatively small in importance compared to those."

"How I can best serve the people of West Virginia is a major consideration," he added. "I have not made up my mind."

The courtly Byrd is highly regarded by his colleagues and, many agree, could not be successfully challenged if he chose to stay on as majority leader. But many say privately that the Democrats need a "new look," and that Byrd is not among the Senate's most telegenic members.

The short list of possible successors includes Sens. Daniel K. Inouye (D-Hawaii), J. Bennett Johnston (D-La.) and George J. Mitchell (D-Maine).