Fairfax County Commonwealth's Attorney Robert F. Horan Jr. said last night that he plans to seek the Democratic nomination for the U.S. Senate from Virginia and expects to make a formal announcement of his candidacy this week.

Although he had been considering the race for some time, Horan said, a principal factor in his decision was the withdrawal last week of Lt. Gov. Richard J. Davis from the confused contest. Davis was the clear favorite of party regulars.

"Once I was sure that the lieutenant governor was out of it," Horan said last night, "then it seemed to me the nomination was something that was possible."

The Democratic candidate to oppose Rep. Paul S. Trible Jr. (R-Va.) for the seat being relinquished by retiring Sen. Harry F. Byrd Jr. (I), will be chosen in less than two weeks by the 3,624 delegates at the party's nominating convention in Roanoke. Trible, a three-term congressman from Newport News, is unopposed for the GOP nomination.

Davis' decision not to make the race was seen as putting pressure on several possible candidates to make known their intentions in the period before the convention.

Others mentioned as possible candidates include state Sen. Hunter B. Andrews of Hampton, Del. Norman Sisisky of Petersburg, and Del. Floyd Bagley of Prince William.

Expressing a belief that Andrews -- a 60-year-old lawyer and the Senate majority leader -- would also enter the race, Horan said he expected that "he'll be the one to beat, probably."

On Saturday, with no Democrat having announced formally for the nomination, Trible poked fun at the disarray in opposition ranks, telling a GOP gathering that he was "the only unopposed candidate for the U.S. Senate in America."

Horan, 49, who is in his fourth 4-year term as chief Fairfax prosecutor, said in last night's interview that he expects the major issue in the general election to be what he described as "the sorry game plan of the administration on the economy."

One of the most disturbing aspects of the Democrats' failure thus far to field any firm candidates, Horan asserted, is that Trible "hasn't had to explain such things as high interest rates, unemployment, the great number of business failures, et cetera, et cetera."

Horan was defeated in 1972 by Rep. Stanford E. Parris (R-Va.) in a race for the House seat from Virginia's 8th District. Defections from Horan by liberal Democrats reportedly helped cause his defeat.

Horan said last night he hoped for "some solid delegate" support from Fairfax, which will send the largest county delegation to the June 4 and 5 convention. Horan said that with most delegates uncommitted, "we've got as good a shot as anybody." He said he has made statewide contacts by heading the Virginia prosecutors' association and by lecturing.

Also prompting him to run, Horan said, was a wish to keep the Senate from becoming a "House of Lords" open only to millionaires.

If he is nominated, he said, his campaign would be "pay as you go."