You are correct there were no “negotiations” leading up to secession, which was unilateral by each state.
There were, however, multiple attempts by various groups to scramble around and craft a compromise that would end the crisis, as had happened in 1820 and 1850, among other years when sectional crises erupted.
Among those attempts there was a Peace Conference and the Crittenden Compromises.
There was even a Corwin Amendment to the Constitution that would forever protect slavery from interference by the federal government within states. The Amendment passed Congress and was sent to the states for ratification. Lincoln expressed no opposition to the ratification of this amendment, though the President has no role in amending the Constitution.