The Treasury Department said yesterday it will need to borrow $14.5 to $17.5 billion during the next two months and announced it would raise $3.7 billion of that next week through note and bond sales.

Deputy Treasury Secretary-designate Kenneth Axelson said the agency does not expect to run the usual second quarter surplus during April, May and June because of the anticipated payout of about $11 billion Carter's program to stimulate the economy.

But Axelson said he does not anticipate having to raise any net new cash during the second quarter either, although the Treasury will have to borrow heavily to keep some money in the till until income taxes come in on April 15.

In the current quarter, the agency said it will raise net new cash of $20 to $23 billion. It already has borrowed $5.5 billion of that. In addition to the offerings it announced yesterday - a three-year note, a seven-year note and a 30-year bond - Axelson said he expects to meet the rest of the Treasury's financing needs through additions to the regular auctions of two-year notes at the end of February and March and an issue of a four-year note early in March.

The Treasury sales announced yesterday include:

$3 billion in three-year notes to be auctioned next Tuesday with a minimum purchase of $5,000. These notes will mature Feb. 15,1980.

$2 billion in seven-year notes to be auctioned Thursday, Feb. 3, in minimum denominations of $1,000. The seven-year notes will mature Feb. 15, 1984.

$750 million of 30-year bonds to be auctioned Friday, Feb. 4, in minimum denominations of $1,000. The bonds will mature Feb. 15, 2007, but can be called in by the Treasury Feb. 15, 2002.

The total $5.75 billion will be used to pay off nearly $2.1 billion in federal securities which mature Feb. 15 and add nearly $3.7 billion to the government's coffers.

Axelson - senior vice-president of J.C. Penney Co., Inc. who served as Deputy Mayor of New York for finance from September 1975 until September 1976 - said the Treasury projects the federal deficit to be $70 billion in fiscal 1977.

He said that calculations for the federal spending year which ends Sept. 30, are based on projections prepared by former President Ford taking account of President Carter's stimulus program and eliminating tax cuts proposed by Ford.

The Carter administration intends to continue the policy begun in the Ford administration of trying to lengthen the average maturity of federal debt.

On other matters, Under Secretary-designate for monetary affairs Anthony M. Solomon said that both the Ford and Carter administrations agree "on the advisability of a floating exchange rate system" for the international monetary system.Under a floating system governments are not required to maintain the value of their currency at a certain level.

Instead, the value of a currency in terms of another is determined by supply and demand in the private market.

Solomon said that there is a question whether the United States wants to resume talks about surveillance of government intervention into foreign exchange markets, but said that such intervention - which interferes with the working of a free-floating exchange systems - is "not a terribly bothersome problem" at the moment.