The number of AIDS cases in New York is expected to double in the next three years, and 3,382 new hospital beds and 2,800 more nurses will be needed to cope with the increase, state health officials say.

In a report on the extent of the AIDS epidemic in New York, the state Health Department said Monday the number of new AIDS cases is expected to double to 10,000.The situation will exacerbate the already severe nurse shortage that has hospitals offering rewards for nurse recruits and a host of benefits to lure nurses.

It also threatens to strain government budgets, since the report found that Medicaid is the principal means of financing AIDS treatment.

The department had no estimate of what the increase in AIDS victims would cost, but said $557 million was spent by government, private individuals and organizations on AIDS research and treatment this fiscal year alone.

The report said Medicaid has paid for the care of 47 percent of the state's 43,683 AIDS patients between 1983 and the end of 1987.

Blue Cross is the next most frequent source of funds, with 26.5 percent of patients.

Patients who pay for their own treatment form the third largest group. However, they constitute only 9.1 percent of all patients.

The report found that the number of AIDS-infected children most of whom got the fatal acquired immune deficiency syndrome from their mothers has risen dramatically.