Former senator Eugene J. McCarthy has authorized a number of old friends and political allies in Minnesota to explore the possibility of his returning to his home state to run against Republican Sen. David F. Durenberger next year.

McCarthy visited Minnesota last month and discussed the prospect of a return to active political life at a series of meetings with some of those old friends and allies.

Yesterday he said the Jerry Eller, a former aide, planned to visit Minnesota in July to measure current political sentiment. "Maybe nothing will come of it," he said of the exploratory effort. But he added that he has told his friends that if there is support for a McCarthy candidacy "I would give it serious thought."

Minnesota Democrats suggested yesterday that the 65-year-old Washington writer and lecturer might have a difficult time gaining the party nomination. "I haven't heard any sentiment for it and I think it would be rather difficult," said Mike Hatch, chairman of the Democratic-Farmer-Labor Party. "He would have to campaign for it rather hard."

Jim Lord, the Minnesota stae treasurer who was present at one of the meetings where a McCarthy candidacy was discussed, said that McCarthy also suffers from a residue of betterness left by the Vietnam war.

In 1968 McCarthy sought the Democratic presidential nomination as an anti-war candidate and refused to support the ultimate nominee, his fellow Minnesotan, then the vice president, Hubert H. Humphrey.

"A lot of people haven't forgotten 1968 and, for rational or irrational reasons, hold McCarthy responsible for Humphrey's defeat," Lord said.

Durenberger was elected in 1978 to complete the term of Humphrey, who died that year. After the 1980 election, there was speculation that former vice president Walter F. Mondale would return to Minnesota to challenge Durenberger. But mondale, who is planning to run for the Democratic presidential nomination in 1984, has since announced that he will not seek the Senate seat.

So far only one Democrat has announced for the Senate race. He is Mark Dayton of Minnesapolis, a wealthy member of the Dayton department store family, which has the financial resources for an extensive campaign.

Others who have expressed interest, according to Hatch, are Rep. Bruce Vento of St. Paul and John Derus, chairman of the Hennepin County (Minneapolis) board of commissioners.

The 1982 elections will be critical for the Minnesota DFL Party. The once-dominant party in the state has suffered a series of defeats in recent years and now has only three statewide office holders: treasurer Lord, Attorney General Warren R. Spannaus and Secretary of State Joan Growe. a

Spannaus, the leading Democratic vote-getter in the state, has announced that he will run in 1982 against Republican Gov. Albert H. Quie, who is considered politically vulnerable.