WASHINGTON — With the departure of top economic adviser Larry Summers, President Barack Obama has a chance to deflect a big criticism often lobbed against his inner circle by the private sector: Lack of CEO chops.

Senior administration officials have said they would like their pool of candidates to include CEOs and business executives.

The business community thinks that is a great idea.

Business executives ranging from Intel CEO Paul Otellini to Citigroup Chairman Dick Parsons have noted the lack of CEOs at the White House. Allstate CEO Tom Wilson, an Obama supporter, went so far as to call the Obama’s dearth of advisers with managerial experience a “hiring mistake for the administration,” in an interview with Fortune last week.

“Under any administration, you want a blend of people on your economic team, some with a business background, some with a public policy background, some with an academic background,” said Robert Nichols, president of the Financial Services Forum, an association for financial chief executives. “You will have a more rigorous debate if you have people with varied backgrounds at the table.”

The White House has been looking for months at chief executives for top economic policy jobs, said Johanna Schneider, executive director of external relations at the Business Roundtable, a lobbying group for executives.

In addition to Summers’ pending departure, Council of Economic Advisers Chair Christina Romer, Office of Management and Budget Director Peter Orszag and Assistant Secretary of the Treasury for Financial Stability Herb Allison have left the administration in recent months.

“It’s not window dressing,” said Schneider, who added that her group has been in touch with the White House about recruiting candidates. “The goal is to bring in somebody with a different set of experiences. They’re generally looking for a business executive who can come in and provide a fresh perspective.”

It’s not like the White House doesn’t talk to executives. Over the summer, Obama met with Berkshire Hathaway’s Warren Buffett, Bank of America Corp. CEO Brian Moynihan and Honeywell International Chairman David Cote, who is on the president’s deficit commission.

Both Otellini and Wilson said they have both participated in off-the-record economic policy discussions with senior White House officials.

However, tensions between the White House and the business community have been fraying, in part because the president spent much of his first two years in office bashing insurers during the health care debate and “fat cat bankers” during Wall Street reform.

The lack of managerial experience at the White House also gives some companies pause, and may be contributing to stymied growth in the private sector, said Mark Calabria, director of financial regulation studies at the Cato Institute.

Even Orszag acknowledged that the lack of CEO power at the White House could be impacting business’ decisions, making them “nervous,” he said in an interview with Charlie Rose last week.

“Regardless of whether they’re legitimate complaints, they are affecting — in a secondary way at least — they’re affecting corporate behavior,” said Orszag, who declined to talk to CNNMoney.com. “You don’t get us … And therefore we’re nervous and therefore we’re not going to hire or make investments.”

Press Secretary Robert Gibbs said Wednesday that chief executives will be in the mix. But he pointed out they have three months to “play the name game,” as Summers won’t be leaving his post as director of the White House National Economic Council until year’s end. He declined to confirm any potential names in the mix.

Executives believed to be in the mix for the Obama economics team include former Xerox Corp. CEO Anne Mulcahy and current Xerox CEO Ursula Burns as well as Citigroup’s Parsons and Honeywell’s Cote.