In a move that could make it the nation's largest book publisher, Gulf & Western Industries Inc. announced today that it will offer about $700 million in cash to acquire Prentice-Hall Inc., a New Jersey-based textbook company.

G&W said it will make a tender offer of $70 a share for Prentice-Hall's 10 million outstanding shares. But sources said the offer comes over the objections of Prentice-Hall management. The Prentice-Hall board is scheduled to consider the offer later this week.

Prentice-Hall stock, traded on the American Stock Exchange, jumped 18 1/4 yesterday to close at 70. The stock also rose 5 points last Friday.

Acquiring Prentice-Hall, the nation's largest publisher of college textbooks with annual revenue approaching $500 million, would represent a near doubling of Gulf & Western's existing publishing base and also would offer entry into the growing personal computer software market. Prentice-Hall has invested heavily in the development of personal computer software and personal computer books.

With more than $4 billion in annual revenue, Gulf & Western, a conglomerate whose holdings range from Paramount Pictures to Madison Square Garden, is already a major presence in publishing through its Simon & Schuster subsidiary.

One of the five largest book publishers in the country, Simon & Schuster posted a 35 percent increase in fiscal 1984 sales to $286 million, profits rising 85 percent to $31.6 million.

Under company President Richard E. Snyder, Simon & Schuster has become known as one of the most aggressive marketers in book publishing. The company once had 11 books on the New York Times bestseller list in a single month,

Earlier this year, G&W acquired Esquire Inc., the nation's 10th-largest educational book publisher, for roughly $180 million, as part of an effort to broaden Simon & Schuster's publishing base.

However, Prentice-Hall is widely regarded by analysts as an underachiever in the industry. Its compounded earnings growth since 1977 has been close to 10 percent -- far below the 18 percent of McGraw-Hill, the nation's largest book publisher, which has diversified holdings in magazines and electronic publishing.

Prentice-Hall earnings per share for the first nine months of 1984 were $2.08 compared with $2.45 for the comparable three quarters last year. Much of the decline has been attributed to start-up costs for the company's personal computer publishing efforts.

Gulf & Western had been examining Prentice-Hall as a takeover candidate for several months, but the chief executive officers of the two companies met for the first time this morning in New York. Sources said G&W initially proposed an offer of $68 a share, but soon increased it to $70 a share.

After the meeting, G&W Chairman Martin Davis sent an open letter to Prentice-Hall President Donald Schaefer outlining the $70-a-share offer and saying "you know I have made numerous requests to explore and discuss fully our proposal for a cash merger. You finally agreed to meet with me this morning . . . " The letter also said that Prentice-Hall would remain a separate entity and that present management would remain.

Prentice-Hall issued a release describing the G&W offer as "unsolicited" and saying it had retained the investment firm of Dillon, Read and the law firm of Cravath, Swaine & Moore to consider the offer. Schafer, who was unavailable for comment, also wanted to caution shareholders not to respond "hastily" to the offer.