Independent presidential candidate John B. Anderson has decided to offer the vice-presidential nomination to former Wisconsin governor Patrick J. Lucey, a liberal Democrat and leading supporter of Sen. Edward M. Kenndey's unsuccessful bid for the presidency, sources close to the Anderson campaign said yesterday.

Lucey told The Washington Post he had not received "a formal offer" but was discussing the possibility with his wife, Jean, at their vacation cabin in Wisconsin.

Anderson himself said yesterday, "I'm not in a position to confirm or deny anything at this point. I've made no particular effort to obscure the fact that Gov. Lucey is one of those who has been talked about. . . ."

Interviewed last night on ABC News, Anderson voiced much admiration for Lucey. "But the selection process is not over," he said as he promised to name his running mate by the end of this month.

The Luceys will be visiting today in Wisconsin with Keke Anderson, wife of the independent presidential hopeful, but Lucey said he had no date for a meeting with Anderson.

Sources close to Anderson said, however, that the decision to offer the nomination to Lucey had been made and all that remained was the timing and circumstances of formalizing it.

In a telephone interview from his Wisconsin vacation spot, the 62-year-old former governor said that as far as he was concerned, the decision on running was in the hands of his wife.

When she took the phone, Jean Lucey said she believed "Anderson is certainly the best of the lot," and was bothered by news stories indicating that his candidacy is "a futile thing.

"If you care about the country," she said, "why not elect the best?"

Anderson and Lucey met in New York last week after Lucey resigned as a delegate to the Democratic National Convention to protest passage of the rule binding delegates to their original candidate commitments. Adoption of the rule effectively sealed President Carter's renomination victory over Kennedy.

Lucey left the Wisconsin governorship in mid-1977 to accept appointment from Carter as ambassador to Mexico, but his personal relationship with Carter -- when both were governors and during his tenure as ambassador -- was never a cordial one.

In the autumn of 1979, White House sources leaked stories criticizing Lucey's service in Mexico. When Lucey resigned in October, he went almost immediately into the just-starting Kennedy campaign as its deputy chairman.

A graduate of the University of Wisconsin and owner of a successful Madison real estate and investment firm, Lucey has found his political career linked with the Kennedys for 20 years.

As chairman of the Wisconsin Democratic Party in 1960, he backed John F. Kennedy against Hubert H. Humphrey in the state's primary election.

A leader in the revival of the Wisconsin party in the 1950s, Lucey was elected lieutenant-governor in 1964, failed in a bid for governor in 1966, and was elected in 1970 and 1974.

His six years as state executive were marked by major tax-reform, economic development and environmental programs and reorganization of the state's widely acclaimed higher- education system.

Lucey has always been identified with the liberal wing of the Democratic Party nationally. He was active in Robert F. Kennedy's 1968 campaign for the presidential nomination and after Kennedy's death became convention floor manager for Eugene J. McCarthy. He was one of those considered as a running-mate for George S. McGovern in 1972.

Anderson has indicated for weeks that he hoped to find a well-known elected Democrat with ties to organized labor as his running-mate.

Lucey would bring those qualities to the Anderson campaign, but insiders conceded yesterday that Lucey is less well-known to voters around the country than might have been hoped.

Nevertheless, Anderson campaign officials said that Lucey had been contacted about the possibility at least a month ago, while he was still working actively for Kennedy, and that discussions had continued through Tuesday of this week.

They said that Anderson himself was showing more strength in the Northeast than any other section of the country and having a midwesterner like Lucey made sense.

Anderson's only other publicized meeting with a possible running-mate came last weekend, when he called on Boston Mayor Kevin H. White, like Lucey, a Roman Catholic. Sources close to White said the vice presidency was not directly discussed, but the mayor's comments afterward indicated skepticism about going on the ticket, though he did not rule it out.

An Anderson-Lucey ticket would lack conventional geographic balance. The Illinois congressional district Anderson has represented as a Republican for the past 20 years borders on Wisconsin, and his home town of Rockford, Ill., is only 75 miles from Madison.

Wisconsin is a target state for the Anderson campaign, because of its progressive political tradition. But it proved a severe disappointment to Anderson in the Republican primary last April, where a third-place finish led to his dicision to leave the GOP nomination contest and run as an independent.

The decision-making role attributed to Jean Lucey by her husband is not a surprise to those who know the family. Like Keke Anderson, Jean Lucey has a reputation as a forceful and outspoken individual and a political force of her own.

Some Democrats who have been close to Lucey over the years had expressed belief that he might be influenced against running with Anderson by his admiration for Vice President Mondale. Lucey said yesterday that "if Fritz Mondale and George Bush were running for president instead of vice president, I wouldn't be considering this other venture." But he added that he had no reluctance to contest them or to meet them in debate.