The Des Moines Register and Tribune Co., publisher of Iowa's largest daily newspaper, is for sale, and may be sold as soon as Jan. 31, the company's chairman said yesterday.

Chairman David Kruidenier made the announcement last night following a decision earlier in the day by the company's board to reject several unsolicited offers made in the last five weeks.

Kruidenier said First Boston Corp., the investment banker retained to evaluate the bids, concluded they were "inadequate."

He said the decision to sell the company was reached after polling stockholders. They said they favor the sale, provided the purchaser is "a high-quality newspaper company which would respect and maintain the journalistic standards of The Des Moines Register, the Cowles family's flagship newspaper."

Kruidenier added that, in the past month, almost all of the nation's major newspaper companies have expressed serious interest in buying The Register, which has a daily circulation of about 240,000. He said that under the circumstances, he was confident that a suitable buyer could be found who would meet all of the qualifications of Cowles family members, who own most of the company's stock.

Some observers were surprised by Kruidenier's announcement, since he had been saying the company was not for sale and would be kept under Cowles ownership.

The company said First Boston is expected to make a recommendation at a meeting scheduled for Jan. 31. In the interim, it appears that First Boston will solicit bids from a list of potential buyers Kruidenier has said includes The New York Times Co., The Washington Post Co., Times Mirror Co. and Knight-Ridder newspapers. Other potential bidders include Capital Cities Communications, Dow Jones & Co., The Tribune Co. of Chicago, Gannett Co. Inc., and the Hearst Newspapers.

No decision was made yesterday about whether the company would be sold to one buyer or broken up and sold in pieces to several buyers. That decision will depend upon which method achieves the greatest value for stockholders.

In addition to The Des Moines Register newspaper, the firm owns several small newspapers, the NBC television affiliate in Honolulu, the ABC television affiliate in Moline, Ill., four radio stations and 14.3 percent of Cowles Media Co. Kruidenier is also chairman of Cowles Media, publisher of the Minneapolis Star and Tribune, which has a daily circulation of about 373,000.

The takeover battle began on Nov. 5, when Dow Jones & Co., publisher of The Wall Street Journal, and several Des Moines businessmen, including two former Dow Jones employes who are directors and employes of The Register, offered $112 million for the company. Since that time, Ingersoll Publications, a Connecticut-based newspaper chain, and Ackerley Communications Inc., a Seattle-based communications company, have submitted bids exceeding the Dow Jones' offer, with the Ackerley bid at $156 million.

The two ex-Dow Jones employes who joined in the first bid were Register and Tribune Co. President Michael G. Gartner and Register Publisher Gary G. Gerlach. On Nov. 9, Kruidenier put Gartner and Gerlach on paid leaves of absence, which he extended yesterday.

Kruidenier yesterday repeated his displeasure with the the surprise bid by the Dow Jones group, but implied a more lucrative offer from Dow Jones would be considered along with the bids of other selected newspaper companies.

Kruidenier said yesterday third- and fourth-generation members of the Cowles family, who are scattered throughout the nation and do not work at the company, are eager to sell their stock. Experts have said the company may be sold for more than $200 million.