Interest rates on new Treasury debt dropped sharply yesterday to the lowest levels this year, the government reported yesterday. The drop in these short-term rates could presage a fall in the key prime lending rate charged by banks from its present 16 1/2 percent to 16 percent, some analysts believe.

Yields on Treasury bills fell to an average of 11.480 percent on three-month bills and 11.677 percent on six-month bills at yesterday's weekly auction, down from 12.189 percent and 12.187 percent respectively the previous week. The three-month bill yield was the lowest since December 21, when auction yields averaged 11.037 percent, while the yield on six-month bills was the lowest since the average of 11.595 percent at the auction of December 14.

Some banks yesterday lowered their broker loan rates, charged to brokers on overnight, secured loans, from 15 1/2 percent to 14 3/4 percent. Manufacturers Hanover and Bankers Trust made this move, which also can be a guide to future prime rate changes.

The administration has forecast a drop in interst rates this year, with an average yield of 11.7 percent on three-month bills. But so far rates have stayed higher for longer than expected by Reagan officials. Persistent high rates have deepened the current recession and added to the cost of servicing the federal debt.

Some analysts have blamed these high rates primarily on the failure of the adminstration and Congress to bring down huge projected budget deficits, while others say that the Federal Reserve's tight money policy has held up the cost of money. The Fed has injected reserves into the banking system in recent days, thus putting downward pressure on rates. However, market analysts disagree about whether this represents a deliberate easing of policy by the Fed or is a response to last week's collapse of Drysdale Government Securities Inc.

Fed Chairman Paul Volcker said last week that money growth was presently "reasonably on track," despite the fact that the narrow money measure is still growing above its target range for this year.

Yields on Treasury bills have dropped by one percentage point in the last three months. After rising sharply earlier this year to 14.74 percent in the middle of February they dropped to 12.43 percent at the end of that month, and then have drifted down bumpily.

The Treasury sold $4.9 billion of six-month and $4.9 billion of three-month bills.

From Tuesday Savings and Loan associations and banks may pay as much as 12.47 percent interest on $10,000 minimum six-month money market certificates, down from 12.71 percent, and 11.48 percent interest on $7,500-minimum 91-day certificates. Banks may pay up to 11.23 percent on the latter.