Attorney General-designate Griffin B. Bell had his first meeting yesterday with FBI Director Clarence M. Kelley amid growing speculation about whether Kelley will be replaced as head of the embattled federal law enforcement agency.

At a press conference Monday, Bell said he had not yet addressed the question of who should head the FBI and added that it would be premature to talk about replacing Kelley before they had even met.

Reliable sources said the private meeting was intended as a get-acquainted session and consisted primarily of Kelley giving Bell a wide-ranging description of FBI activities. Bell is in Washington this week for a series of briefings on Justice Department responsibilities.

Despite Bell's comments there have been repeated rumors that he and President-elect Jimmy Carter plan to replace Kelley. It was reliably reported two weeks ago that the FBI post had been offered to Frank Johnson, a federal district judge in Alabama, but that he had turned it down.

Others mentioned include Patrick Murphy, former head of the police in Washington and New York City; Henry Ruth, a former Watergate special prosecutor; John Doar, special counsel for the House Judiciary Committee during the Nixon impeachment hearings, and Mitchell Rogovin, who served as attorney for the Central Intelligence Agency during the Senate intelligence hearings.

There also have been reports that some influential Democrats in Congress have recommended to the Carter camp that Kelley be kept on, at least until Bell has had a chance to evaluate his performance over a period of months.

Kelley, who became director in July 1973, is known to want to stay in the director's job. He is understood to be hopeful of remaining at least until October because of the difference that would make in hid federal pension rights.

Kelley, now 65, retired from the FBI in 1969 after 20 years' service to become police chief in Kansas City, Mo. Under a federal law passed last summer, the three years he now has served as director would allow his pension to be recomputed on the basis of the higher director's salary.

However, the law does not take effect until Oct. 1, and Kelley would have to remain in active federal service until that date to take advantage of its provisions.