The comedian and actor, 48, is facing allegations of rape, emotional abuse and sexual assault.
Channel 4 launched an investigation into his time at the channel after he was accused of pursuing audience members for sex while presenting the broadcaster’s Big Brother spin-off shows.
Brand has strongly denied the allegations, in a video posted online on Friday, saying he has been “promiscuous” but all of his relationships have been “consensual”.
Culture, Media and Sport Committee chairwoman Dame Caroline Dinenage wrote to broadcasters on Tuesday, including Channel 4, to request further details on what actions they are taking in response to the allegations.
Dame Caroline asked for the broadcaster to set out the time for completion of the investigation and urged it to “disclose” the information that can be made public.
In a letter to the commons committee on Monday, and published on Tuesday online, Channel 4 chief executive Alex Mahon said: “Since becoming aware of some of the allegations, just over a week ago, we have carried out extensive document searches and thus far have found no evidence to suggest the alleged incidents were brought to the attention of Channel 4 management at the time.
“We will continue to look at this issue and will forensically examine any further information, including the accounts of those affected.”
It comes as BBC Director-General Tim Davie ordered a review into Russell career at the corporation in light of the allegations made against him.
The review, headed by its director of editorial complaints Peter Johnston, will look at the allegations against Brand and what was known about them during his time at the BBC.
The comic worked for BBC radio between 2006 and 2008 as well as appearing on other shows.
In a question and answer session with staff, Davie said they were dealing with “very serious allegations”.