The chairmen of several House legislative committees have begun a campaign to have a Democrat named as the next director of the Congressional Budget Office, blocking the possible appointment of Rudolph G. Penner, a Republican economist at the American Enterprise Institute.

Penner, chief economist at the Office of Management and Budget in the Ford administration, is widely regarded as the front-runner to replace Alice Rivlin, who did not seek reappointment when her four-year term expired in January. She is still at her job pending appointment of a successor.

The committee chairmen, many of whom would like to modify the budget process to give their committees a much larger say in budget matters, are circulating the draft of a letter addressed to Speaker Thomas J. "Tip" O'Neill in which they back Rivlin's three former deputies for the post. Four chairmen, Rep. John D. Dingell (D-Mich.) of Energy and Commerce, Carl D. Perkins (D-Ky.) of Education and Labor, James J. Howard (D-N.J.) of Public Works and Transportation, and Augustus F. Hawkins (D-Calif.) of Administration, had signed the letter as of yesterday, House sources said.

The men recommended are Robert A. Levine, a vice president of System Development Corp., a California computer firm, who was Rivlin's deputy from 1975 to 1979; Robert D. Reischauer, a senior vice president of the Urban Institute, who was Rivlin's special assistant for three years and deputy director from 1979 to 1981; and Raymond Scheppach, executive director of the National Governors Conference, who went to work at CBO in 1975 and was deputy director from 1981 until early this year. Scheppach has indicated he may not be interested in the job.

Each of the three has the experience needed to "maintain the tradition of non-partisan excellence established by Ms. Rivlin" and "the integrity of the process," it added.

Rivlin, who did not seek a third four-year term, is a Democrat. She will become director of economic studies at the Brookings Institution later this year.

In a separate letter to O'Neill, Rep. Fernand J. St Germain (D-R.I.), chairman of the House Banking, Finance and Urban Affairs Committee, also backed the same three men. St Germain did not mention Penner by name, but argued that the new director "must be free from any narrow economic dogma. For instance, I think it is important that the new director is not a doctrinaire monetarist."

By law, the Speaker and the President-pro-tem of the Senate, who is Sen. Strom Thurmond (R-S.C.) make the appointment jointly upon the recommendation of the House and Senate Budget committees, but a joint nominating group of committee members has yet to meet.