The Treasury plans to raise $26.8 billion during this quarter to finance the growing federal budget deficit, the department said yesterday.

Deputy Treasury Secretary Robert Carswell said the Treasury will have to raise between $21 billion and $25 billion in the fourth quarter as well. Moreover, the department expects a "significant additional deficit and hence additional financing requirements for the first quarter of 1981," Carswell said.

Some financial market analysts are worried that the huge demand for funds by the federal government, coming on top of a large and growing slate of long-term bond issues by corporations, could squeeze the markets. At the least, many analysts are predicting long-term interest rates will not decline further this year and could rise.

Rates have firmed in recent weeks as the volume of corporate and tax-exempt bonds issues has grown. With the certainty of a large budget deficit and the possibility of a significant tax cut, which in the short run would worsen the deficit and increase federal borrowing needs, bond prices have fallen and interest rates have increased.

Carswell said the Treasury plans to raise $3.2 billion in new cash through a sale of notes and bonds next week.

It will sell $8.25 billion in securities, including $4 billion in 3 1/4-year notes maturing Nov. 15, 1983, at an auction next Tuesday.Next Wednesday it also will sell $2.75 billion in 10-year notes maturing Aug. 15, 1990. The following day it will offer $1.5 billion in 29 1/4-year bonds maturing Nov. 15, 2009.

From the proceeds, the Treasury will pay off $5.05 billion in maturing securities, leaving $3.2 billion new cash.

With these proceeds, the Treasury will have raised $13.8 billion of the $26.8 billion it needs for the current quarter, leaving $13 billion in new money to be raised later, Carswell said.