The Tennessee Valley Authority yesterday said it had rejected a final proposal for a compromise settlement of the legal battle pitting a tiny fish, the snail darter, against a huge TVA project, the Tellico Dam.

But a significant dissenting view within TVA's board of directors raised the possiblity that TVA's long-standing position in support of completing the Tellice project might soon be changed.

In a statement released at its Knoxville headquarters, Board Chairman Aubrey J. Wagner said he had written to Interior Secrtary Cecil D. Andrus rejecting Andrus' proposal for new consultations on the Tellico project and the snail darter, a fish species that could become extinct if the dam is completed.

Only a few hundred snail darters are known to exist, and they all live in the shallows of the Little Tennessee River south of Knoxville. They could not survive if their shallows were engulfed by the Tellico Reservoir.

Accordingly, a federal appeals court last year decided that the dam would violate a federal law that prohibits any governmental action threatening "endangered species" of life such as the snail darter. The court stopped work on the $127.5 million dam, which was more than 90 percent completed.

On April 18, the Supreme Court is scheduled to hear arguments on TVA's appeal of that decision. It was the impending oral argument that prompted Andrus last month to write TVA's board proposing one more round of discussions toward a settlement of the dispute.

In his statement yesterday, TVA Chairman Wagner said he had turned down Andrus' request, citing congressional appropriations acts calling for completion of Tellico.

Wagner said a second board member, William L. Jenkins, shared his view.

But the third member of the TVA board, S. David Freeman, broke with his colleagues in a separate letter to Andrus.

Freeman expressed a willingness to compromise, noting - in a statement that conflicts with TVA's long-standing position on the subject - that creation of the reservoir, which would doom the snail darter, "is not vital to the Tellico project."

Although Freeman represents a minority on the issue, that position could change quickly. Wagner, the chairman will leave the board when his present term expires on May 18. His successor will be appointed by President Carter, and it was Carter who appointed Freeman to the board last year.

"The same guy who appointed Dave Freeman is going to appoint the new member," said a Senate staffer who has followed the Tellico case closely. "Everybody assumes that Freeman's going to be in the majority pretty soon," the Senate aide added. He asked not to be quoted by name.

Freeman said yesterday he has been frustrated by the TVA's refusal to consider any compromise solution of the dispute. "I think we should depart from the position that there are only two ways - the TVA way and the wrong way," he said in an interview.

The Tellico case has become a symbol of the struggle between the interests of development and environmental protection. Opponents of federal environmental regulations say the case of a relatively obscure fish species stopping a major flood control and hydroelectric power project, shows that environmental protection has been over-emphasized.

Freeman's letter suggested compromise that could preserve cetrain uses of the dam without eliminating the snail darter's habitat. He proposed that Tellico be used as a "dry dam" - with its gates normally left open so that no permanent reservoir would be created.

The gates could be closed when floods were threatened, Freeman said. Thus the dam would serve one of its intended functions - flood control - but would not offer the hydroelectric power or the recreational reservoir it had been designed to provide.