LEAD: Reports circulated throughout the accounting industry today that two of the biggest firms - Ernst & Whinney and Arthur Young & Company - would soon announce a merger that would create the world's largest accounting firm.

Reports circulated throughout the accounting industry today that two of the biggest firms - Ernst & Whinney and Arthur Young & Company - would soon announce a merger that would create the world's largest accounting firm.

The most detailed report came in an article that will be published Thursday in Bowman's Accounting Report, a leading industry newsletter. The article reports that the governing councils of the two firms have agreed to merge and that partners of Ernst & Whinney and Arthur Young would soon be asked to vote on such a combination.

A senior Ernst & Whinney partner, who asked not to be named, said tonight that a special meeting of the firm's New York partners had been scheduled for Thursday and that ''an announcement can be expected from the firm over the weekend.'' He said he was not told the subject of the meeting. 'It's News to Me'

Two people who work as advisers to the firms said work slowed considerably at a number of offices of both firms as lower-level staff members learned of the reports and stopped in hallways to exchange notes.

Carl D. Liggio, general counsel of New York-based Arthur Young, said of the reports, ''It's news to me.'' He added that rumors of a merger with Ernst & Whinney had been swirling for months.

Telephone messages left at the New York home of Ray Groves, Ernst & Whinney's managing partner, were not returned. Michael Grobstein, an Ernst & Whinney vice chairman, said, ''Our firm never comments on reports of this type, and we never will.''

The Bowman's article said the fine points of a merger were worked out on Monday, when the two firms' top officials met in secrecy on the 23rd floor of Arthur Young's Park Avenue headquarters, guarded by Pinkerton security men.

The article said that Arthur Young's managing partners learned of the deal in a closed-circuit televised conference today; that the firm's remaining partners would be briefed Thursday and Friday, and that William Grant, one of two managing partners of Arthur Young, would head the combined firm as managing partner, with Mr. Groves of Ernst & Whinney serving as chairman. 'Multiple Sources'

''The executive committees have a merger deal worked out,'' said Arthur Bowman, the editor of Bowman's. He also said he had obtained his details from ''multiple sources within the firms.''

The most recent merger situation involving two Big Eight accounting firms arose in 1985, when efforts to combine Price Waterhouse and Deloitte, Haskins & Sells were rejected by partners of the firms.

A merger between Arthur Young and Ernst & Whinney would create a vast professional services firm that would be the largest in the world based on a number of criteria.

Ernst & Whinney is the world's fifth-largest accounting firm, with $2.2 billion in revenues. Arthur Young ranks sixth, with $2.1 billion.

Together, their $4.3 billion in revenues would exceed those of the current world leader in billings -KMPG/Peat Marwick, which in 1988 had revenues of $3.9 billion. In the United States, the combined firm's $2.02 billion in revenues would be slightly larger than those of the current leader, Arthur Andersen & Company, which last year reported revenues of $1.71 billion.

The combined firm would have 2,100 partners in the United States alone. This would place it ahead of Peat Marwick, the current leader, which has 1,900 domestic partners.

By analysts' best estimates, roughly 45,000 people would work at a combined firm. And their 500 offices would be spread out in just about every developed nation.

''A merger would be great for both firms,'' said James Emerson, the editor of another industry newsletter, the Big Eight Review. ''Ernst & Whinney has not had a good international presence, and that is critical now. One of Arthur Young's strengths is that it has a tremendous international organization.'' Greater Presence in Europe