Price competition for corporate audits is hurting accounting firms so much that they are seeking new sources of revenue, and in some cases merger partners.

Price Waterhouse & Co. and Deloitte Haskins & Sells were reported this week to be discussing a merger. The Wall Street Journal quoted an anonymous Deloitte official as saying that the company was attempting to gain strength in management consulting to avoid losing its clients.

Price is the fifth-largest of the Big Eight accounting firms; Deloitte is the seventh. A merger would make it the biggest in the industry.

Executives of both firms declined to comment on the report.

Another rumored merger among Big Eight firms is that of Arthur Young, the sixth-largest, and Touche Ross & Co., the eighth. However, industry sources said yesterday that a deal was unlikely.

The largest merger that has taken place in the industry recently was that of McGlabrey Hendrickson, ranked 13th, and A. M. Pullen, ranked 18th. The combined firm now ranks 12th. Industry sources said other second-tier accounting firms were also seeking merger partners.

Audit contracts are solicited by competitive bidding and usually are billed on an hourly basis, typically $150. Computerization has cut back the time required to do audits, and much of the work can now be done by lower-paid staff.

According to a survey by Public Accounting Report, a trade publication based in Atlanta, 36 percent of the public companies changing auditors last year did so to cut costs, compared with 27 percent in 1982.

Audits used to represent 70 to 75 percent of Big Eight revenues. Arthur Bowman of Public Accounting Report, an industry newsletter, predicted that share would drop to 55 to 60 percent in the next few years.

He noted that Price's audits represented 65 percent of its revenue in 1983, compared with 67 percent the previous year. Its total revenue increased 4 percent, from $475 million to $493 million during the period, the smallest increase for any of the Big Eight. For Deloitte, the percentage of revenue from audits fell from 73 to 71 percent in 1983. Total revenue increased 10 percent, from $390 million to $430 million.

While some accounting firms do tax returns, the biggest development in the past five years has been in management consulting. This is potentially a more creative -- and therefore lucrative -- business than auditing. It also enables accounting firms to retain a relationship with clients between audits.