The idea may not have drawn strong support on Capitol Hill, but the White House is not about to give up on the president's drive to turn over more government functions to private industry.

The Office of Management and Budget this week will name Ronald Utt, a senior economist with the U.S. Chamber of Commerce, to a new position overseeing the administration's "privatization" efforts. And the White House today is expected to name a bipartisan commission to generate public support for the campaign.

Despite President Reagan's strong support for such efforts, Congress has shown little interest in any of the administration's major privatization proposals, which call for selling some naval petroleum reserves, the Bonneville Power Administration and some Amtrak rail service in the Northeast.

The president announced in a July 4 speech that he would create a commission to identify government programs that should be turned over to private industry. David Linowes, a University of Illinois economist, has been mentioned as the person most likely to head the commission. White House officials have announced that Linowes will brief reporters today in Santa Barbara, Calif., on the president's renewed efforts to press for a greater reliance on private business.

The privatization campaign is part of the president's "Economic Bill of Rights," which calls for Congress "to prune judiciously from the government that which goes beyond the proper realm of the state."

Utt resigned this week as deputy chief economist at the Chamber. Officials said he will be an associate director at OMB.

The economist has worked for the chamber since 1980. He was previously research director for the National Association of Real Estate Investment Trusts. Before that, he was a senior economist at OMB and director of the housing finance division at the Department of Housing and Urban Development. Utt has a doctorate in economics from Indiana.