Sen. Adlai E. Stevenson III (D-III.) had decided not to run for reelection in 1980 and is instead leaning, more than ever, toward running for president, it was learned.

Moreover, the likelihood of his seeking the presidency will increase if President Carter continues to mishandle -- in Stevenson's view -- the vital business of the nation at home and around the world.

Stevenson said in an interview that he has undertaken no organizational eforts for a presidential campaign, nor raised any funds. In fact, he said, he has returned some unsolicited "grassroots" contributions and has declined some larger fund offers, because he wants first to sort out his thinking on a challenge to Carter.

For now, he said, he will continue to take soundings on whether there is a constituency for his ideas and candidacy againt Carter, whose agenda he sees as little different from Republicans Dwight D. Eisenhower and Gerald R. Ford.

Stevenson said he will announce his decision soon, probably within a few weeks. However, sources close to him indicated he wants to delay a short time so that it would not seem that his decision not to run was prompted by the entry into the 1980 GOP Senate primary last week by Illinios Attorney General William J. Scott.

Stevenson alerted Carter to his decision on another Senate term last July, and repeated his plans to the president in November at a private lunch at the White House. About that time, he also began publicly musing about the possible need for a third party to provide direction for the country that the two existing major parties were failing to give.