Mr Phillips insists the commission is continuing with its work
MPs are set to look into the running of the Equality and Human Rights Commission (EHRC) after a spate of resignations of senior officials.
Six commissioners have left the body in the past four months, increasing the pressure on chairman Trevor Phillips.
The communities and local government committee is set to investigate how the watchdog is run later this year and may ask Mr Phillips to give evidence.
One Labour MP said this was justified as the body was "clearly in trouble".
Emily Thornberry, a Labour member of the Commons communities committee, said she expected MPs to look into the matter when Parliament returns from its summer recess in October.
"Clearly it is an organisation in trouble and it is completely reasonable for us to do an inquiry into what has been going on there," she said.
Parliament's joint human rights committee is also reportedly considering a separate inquiry.
Mr Phillips was appointed to a second term as commission chairman this month and still has the backing of ministers.
However, a series of resignations of senior officials and reports of internal splits have raised question marks about how the organisation is being managed.
Several influential figures, such as Stonewall's Ben Summerskill and Mencap president Lord Rix, have urged Mr Phillips to quit.
On Tuesday, Labour MP Rob Marris joined those calling on him to step down.
In a letter to the Guardian, Mr Marris said the commission's slowness in responding to a complaint he made about the failure of certain sports organisations to confront racism demonstrated its "dysfunction".
He accused the commission of not showing a "serious approach either to tackling racism or to democracy and elected representatives".
"I urged the government not to reappoint Mr Phillips," he wrote.
"Regrettably, they did. If he won't resign, it is time he is dismissed."
Mr Phillips maintains the organisation's work will not be compromised by the recent high-level departures.
Formerly the head of the Commission for Racial Equality, Mr Phillips remained as chairman when the organisation expanded in 2006 to cover the issues of age, religion and belief, sexual orientation and the promotion of human rights.