COLUMBUS, OHIO, AUG. 24 -- Gov. Richard F. Celeste said today that he has decided against running for the 1988 Democratic nomination for president.

Celeste, with his family nearby, made the announcement at a news conference at the governor's mansion in suburban Columbus. He said he concluded that a presidential bid at this stage would cost too much and take too much of the time he needs for running the state.

Celeste had announced in the spring that he was considering seeking the nomination.

Since then, he said, he had talked with advisers and other supporters and decided he could spread the state's message better if he remained governor.

Celeste estimated that a presidential campaign would cost $6 million and an investment in time that "would be so substantial that Ohio's message would be overshadowed."

As governor, Celeste has concentrated on altering Ohio's image as a "Rust Bowl" state by attracting industry. The new jobs cut the state's unemployment rate from 14 percent when he took office in 1983 to slightly more than 7 percent last month.

But Celeste also raised taxes heavily and was criticized by business leaders for a pro-labor image and troubles with the Ohio workers' compensation system.

Celeste, 49, is among a handful of Ohioans who have expressed interest in the 1988 race. Sen. John Glenn (D-Ohio) says he is considering a presidential race, but only if he can retire a debt from his unsuccessful 1984 race. Rep. James A. Traficant Jr. (D-Ohio) said last week that he had authorized formation of a committee to explore a presidential bid.