The Reagan administration, in what would be its first such response to the prolonged recession, indicated yesterday that it may reverse itself and support some extensions of unemployment benefits to workers who have exhausted their entitlements.

The administration up to now has resisted proposals for special anti-recession aid to the housing industry, farmers and other victims of the recession.

Its indications that it may reverse position on unemployment benefits--it said just a week ago that it opposed extensions--comes at a critical time both politically and economically.

The election is three months away; the unemployment rate in May was 9.5 percent, the highest since the Depression. And in May, according to Labor Department figures, only 43 percent of the nation's unemployed workers were receiving unemployment benefits, compared with 68 percent in March, 1975, at the height of the last recession.

Experts said this decline was due in part to eligibility changes pushed through Congress last year by President Reagan.

A White House source said the president has not endorsed any specific extension proposal yet. But he said the administration is discussing some compromise with members of the Senate Finance and House Ways and Means committees now in conference on a major tax and benefit bill. Members of both committees have supported extensions.

Two compromises are under discussion.

One involves an eligibility change voted last year and scheduled to take effect Sept. 25; it would alter the triggering mechanism to make it harder for states to qualify for an extra 13 weeks of unemployment aid on top of the basic 26 weeks to which all insured workers are entitled. If the new mechanism takes effect as scheduled, up to a dozen states and hundreds of thousands of workers would be dropped from the extra-13-weeks program on Sept. 25 or shortly afterward. "We are sympathetic to that problem," said one administration spokesman.

The second issue is whether on top of their basic 26 weeks and extra 13 under existing law, workers in high-unemployment states should be allowed even further assistance, 10 to 13 weeks more of benefits, for a total of 49 to 52 weeks.

One urgent motive for all concerned, one congressional source said, is to sweeten the tax bill for members of Congress from high-unemployment states and thereby help assure passage when the conference report goes back to House and Senate for final approval.

Both Senate Finance Chairman Robert J. Dole (R-Kan.) and House Ways and Means Chairman Dan Rostenkowski (D-Ill.) made clear Tuesday they think the tax bill may be in danger, especially in the House, where many members are reluctant to vote for tax increases in an election-recession year.

"Thirteen states means 90 votes," a congressional source said; one proposed compromise on unemployment insurance would benefit 13 states. But the same source said if the White House insists on paying for the extra unemployment insurance by cutting other social programs, there would not be a deal. The main objection of the White House has been to the likely cost of extensions.

One proposed plan, under discussion earlier this week, had an estimated price tag of $750 million in fiscal 1983. It would suspend the Sept. 25 effective date for several months, and provide 10 to 13 weeks extra on top of the first extra 13. Administration sources said that most of the $750 million cost came from the first of these two proposals.