The FBI is investigating a $20.5 million, no-bid contract awarded by Chicago Public Schools to a Wilmette company and what role CPS CEO Barbara Byrd-Bennett played in it, according to a source familiar with the matter.

Byrd-Bennett previously worked for the company, SUPES Academy, which trains school principals, before Mayor Rahm Emanuel appointed her as CEO of the financially beleaguered district.

The FBI and the U.S. attorney’s office in Chicago have been investigating the contract for more than a year, the source said. A grand jury has taken up the probe, the Sun-Times has learned.

Meanwhile, two City Hall sources told the Sun-Times that Byrd-Bennett’s $250,000-a-year contract, set to expire in June, has not yet been renewed nor will it be unless the investigation is cleared up. Hired in the wake of the 2012 teachers’ strike, Byrd-Bennett remained on the job Wednesday, a district spokesman said.

The awarding of the $20 million contract has repeatedly drawn sharp criticism given the perilous finances of the school system, and principals have griped about the quality of the training they received.

Byrd-Bennett did not return messages for comment Wednesday.

A spokesman for SUPES late Wednesday said the feds had obtained records and files from the company and informed it of the investigation.

“SUPES will of course cooperate with this investigation. At the same time, the company stands behind the countless hours of training it has provided to Chicago Public Schools principals. Principals are the key to improving schools, and SUPES’ peer-to-peer leadership training shares the best practices of school leaders from around the country,” said Dennis Culloton, a spokesman for the company.

The Chicago Board of Education would confirm Wednesday only that federal authorities are investigating “a matter” at Chicago Public Schools but declined to elaborate.

In a vague, emailed statement, Board of Education President David Vitale said the board was informed Tuesday of an investigation and of the feds’ request to interview several employees.

“We take any allegation of misconduct seriously, and we are fully cooperating with investigators who requested that we not discuss any specifics regarding the ongoing investigation,” he said.

In the district’s largest no-bid contract in recent memory, SUPES received the contract from CPS to provide ongoing training on Saturdays for principals and network chiefs through 2016 at a cost of $20.5 million. According to the contract, the company was supposed to use experts who’d specialize the training according to the type of school the principal led — including schools set to receive children affected by the massive 2013 school closings.

It didn’t take long for the no-bid deal — approved unanimously in June 2013 by the mayor’s school board — to ignite criticism, especially as the district stared down a $1 billion budget deficit that year.

By October, principals were complaining about the quality of professional development they were receiving from SUPES, according to a newsletter produced by the Chicago Principals and Administrators Association.

The Principals Association “is sorry to report our members, in large numbers, are expressing dissatisfaction with the caliber of the `SUPES’ Academy,” the Association’s October 2013 newsletter said.

“The quality of the workshops is the most serious and frequent complaint we receive,’’ the newsletter reported. Other gripes: “The principals feel the presenters are not sufficiently knowledgeable regarding developing high-quality leadership in such a large/diverse urban district.”

However, the newsletter reported that the “necessary CPS staff” had agreed to meet with the Principals Association on the matter.

Following a June 2013 story by Catalyst-Chicago detailing Byrd-Bennett’s employment history with the company, the CPS inspector general opened an investigation. Before CPS hired her full-time to replace Jean-Claude Brizard, Byrd-Bennett worked as a paid coach for SUPES while collecting a $21,500-a month paycheck from CPS as a contract education adviser to Brizard, Catalyst has reported.

The current CPS inspector general, Nick Schuler, declined to comment on any aspect of his office’s investigation.

Chicago Public Schools has already paid the company nearly $5.9 million so far this fiscal year, and a total of almost $15 million since 2012 on the no-bid deal and other, smaller contracts, according to CPS’ procurement website.

For weeks, CPS has dodged the question of whether Byrd-Bennett’s three-year contract would be renewed for the mayor’s second term.

After Wednesday’s City Council meeting, Mayor Rahm Emanuel said he did not know enough about the matter to comment — or to give a vote of confidence to Byrd-Bennett.

“I don’t even know who they’re looking at. It’s a CPS matter,” Emanuel said.

“The federal authorities that are investigating don’t share a lot while they have an active investigation. So I’m as eager as you are for answers to questions. [But] I’m not the person that can provide them at this moment,” Emanuel said.

Emanuel said he spoke to Byrd-Bennett briefly before Tuesday’s luncheon marking the Chicago Public Education Fund’s 15th anniversary, and “she said the authorities are looking at a matter at CPS. Then I had to go into the luncheon to give a speech.”

Contributing: Kim Janssen, Becky Schlikerman, Jon Seidel, and Tina Sfondeles

SUPES Academy Contract