Several leading Republicans have asked Rep. Stanford E. Parris (R-Va.) to consider running for the U.S. Senate seat being vacated by Harry F. Byrd Jr. (I-Va.), saying they believe the leading contender, Rep. Paul S. Trible Jr., cannot win.

Word of the offer to Parris surfaced here last night at a tribute to the politically reluctant Gov. John N. Dalton, the first choice of party leaders who seek to block Trible's bid. Today, Parris confirmed the meeting and said he is "intrigued" by the proposal.

Trible, 34, has been exploring a Senate race for more than a year, but he is viewed by some party elders as too much a mirror image of defeated GOP gubernatorial candidate J. Marshall Coleman.

One of the men involved in the "anyone-but-Trible" search said, "We've just been through an articulate-young-man year" in the recent Democratic sweep of statewide offices. If Coleman, 39, had been 66 and lost, "Trible would be a shoo-in," the strategist said. The men who met with Parris at a luncheon yesterday at the Maison Blanche Restaurant near the White House to discuss the matter asked that their names not be used because the race is still wide open.

Parris, 51, has the leathery look of experience that would appeal to older party leaders. He also has the reputation of being a good fund-raiser and is close to Dalton, whose term expires next month. Parris was his seatmate in the General Assembly and served in the Dalton administration as Secretary of the Commonwealth and Washington liaison officer before returning to Congress.

Parris also won election by a narrow margin in 1980 and is viewed by some Republican strategists as vulnerable in his expected rematch with former Democratic Rep. Herbert E. Harris II, who unseated Parris in 1974 and lost to him in the Reagan landslide.

Parris said he called Dalton on the day Byrd announced he would retire and that Dalton told him "unequivocally and immediately that he was not remotely interested" in the Senate seat.

Yet, at the Dalton tribute speaker after speaker paraded to the rostrum to praise Dalton and to express the hope that someday he will again be a candidate for statewide office. But Dalton, 50, sent no approving signals in response and friends said he is giving them no encouragement privately, insisting that he is determined to enter private law practice here.

Parris said that between now and the first of the year he will "try to see how much fire is behind the smoke" of the proposal that he run. One reason Parris might be reluctant to make the Senate race is a fear of turning his House seat over again to Harris.

But the men at the luncheon promised him that they would find a suitable challenger to Harris.

Parris boosters reason that if he can beat the liberal Harris in the 8th District, a swing district with a substantial moderate-to-liberal electorate, he can defeat a similar Democrat, such as 1978 Senate loser, Democrat Andrew P. Miller of Alexandria, in a statewide contest.

Parris already has budgeted $600,000 for next year's House race, which is about one-fourth of the cost of a Senate race. "He'll have no trouble raising that in just one-tenth of the state," a Parris aide said. "So if you're going to get into a cage with a gorilla, why not go for the championship?" he asked.

Parris had the requisite praise for Trible, calling him "a very nice young man, very capable." But friends of Parris said, "Stan is a pretty combative guy" and given the proper incentive, he wouldn't shy away from challenging Trible at the spring precinct caucuses or next summer's state party nominating conventions.

Some of those encouraging Parris, however, may only be using him as a stalking horse to get Trible out of the race. Many Republicans said they would prefer either of two other members of the state's House delegation, retiring 6th District Rep. M. Caldwell Butler or Trible's Tidewater colleague, G. William Whitehurst. But neither of them has expressed interest in a head-on fight with Trible.

Whether Trible would withdraw voluntarily is unclear. He is popular among the New Right and with the Reagan administration and observers said he is confident he can raise the money required to make him better known across the state.

But one party leader said that if State Party Chairman Alfred B. Cramer III, Sen. John W. Warner, former Gov. Mills E. Godwin and Dalton "sat down in a room with Paul and told him he could not win and asked him to withdraw he would. He's an intelligent young man and he knows he'd only be 40 when the seat came up again."