Mr Phillips has headed the EHRC since it was created in 2006
Equalities chief Trevor Phillips faces a possible investigation by Parliament over claims he tried to influence a committee drawing up a report.
The joint human rights committee said he had spoken to at least three of its members about its draft report.
It was investigating the Equalities and Human Rights Commission [EHRC] after several commissioners resigned.
The EHRC said it was unaware of any reason why his actions would amount to contempt but was happy to co-operate.
The joint committee of MPs and peers published a special one paragraph report on Wednesday saying that at the start of their meeting on 9 February, it had emerged Mr Phillips had "recently spoken to at least three members" about consideration of a draft report and the publication of written evidence.
"In our view these discussions could constitute a contempt of both Houses in that they may be an attempt to influence the views of certain members of the committee shortly before it considered a draft report directly relevant to Mr Phillips in his role as chair of the EHRC," it said.
"We recommend that the matter should be subject to investigation by the privileges committees of both Houses."
Committee chairman Andrew Dismore said that he had submitted a formal request to Commons Speaker John Bercow for the matter to be put to MPs.
Mr Bercow will need to decide whether to grant it parliamentary time - MPs would decide whether it should be investigated by the standards and privileges committee.
It is rare for non-politicians to be investigated for contempt of Parliament - the last to be called to the House to be formally rebuked was Sunday Express editor John Junor in 1957.
But in January the Commons backed a contempt investigation into a law firm which Lib Dem MP John Hemming had complained had tried to intimidate him.
The joint committee on human rights decided to hold an inquiry into the EHRC in July 2009, following resignations by four commissioners and the chief executive within months.
Former commissioners have told the inquiry there was a "culture of intimidation" and a "clique that the chair surrounded himself with".
But in his evidence to the committee in December, Mr Phillips said "arguments" and "passions" were part of the EHRC's role as it was dealing with difficult issues.
In a statement about the committee's allegation of contempt, the EHRC said: "Neither Mr Phillips nor the commission is aware of any reason why any of his actions might amount to a contempt of the Houses of Parliament.
"Should the parliamentary authorities decide to take this matter further both Mr Phillips and the commission would be happy to cooperate fully."