Gov. Cliff Finch will "leave no doubts" at a news conference today that he is running as a Democrat for the Senate seat to be vacated by veteran Sen. James O. Eastland (D-Miss.), it was learned yesterday.

"He will erase any doubt about his plans," said a top Finch appointee and one of Finch's closest political advisers. "But it will fall short of an actual announcement to run."

When asked if Finch was simply floating a trial balloon, another top Finch aide responded, "You can go stronger than that. He con't announce, but he'll leave no doubts that he's running."

Finch would join a field of Democratic candidates now headed by his predecessor, former governor Bill Waller, who formally announced his candidacy a day before word spread that Eastland would not seek a seventh consecutive term. The Democratic primary is scheduled for June 6.

Other candidates who have announced their intentions to run as Democrats are Dr. Robert L. Robinson, former head of the state's industry-seeking Agricultural and Industrial Board in the Waller administration; black activist Henry Jay Kirksey, and state Rep. Richard C. (Sonny) Tedford of Marks.

Eastland's political activity among several pouular Republicans, most of whom were spending yesterday making phone calls and assessing their chances.