The Treasury Department plans to borrow $30 billion next week to replenish the government's coffers, although the auctions will not include any 30-year bonds. Every three months, the government holds three debt sales to finance the $2.6 trillion national debt. It normally sells three-year notes, 10-year notes and 30-year bonds. However, Treasury officials said Wednesday that the 30-year bond will not be part of next week's auction because President Reagan has not yet signed a tax bill with a provision needed to give the government authority to issue any more such bonds. William Bremner, deputy assistant treasury secretary for finance, said the tax bill, which cleared Congress right before adjournment, has not yet reached Reagan's desk. He said if the president does get the measure in the next few weeks, the Treasury will auction a new batch of 30-year bonds totaling $9 billion later this month or in early December. If the Treasury does not get the authority, Bremner said the government will offer a second short-term debt instrument known as a cash-management bill. The auctions for next week call for: _$9.5 billion in three-year notes in minimum denominations of $5,000 to be auctioned Wednesday. _$9.5 billion in 10-year notes in minimum denominations of $5,000 to be auctioned Thursday. _$11 billion in a 37-day cash management bill to be auctioned Thursday in minimum amounts of $1 million. These bills are purchased by security houses.