He made the comments on BBC Radio Ulster's Inside Politics programme.
It is understood that Sinn Féin have proposed an individual to chair the new talks process.
It is believed the name has been forwarded to the British and Irish governments but there has not yet been a response.
A number of politicians strongly criticised the handling of previous negotiations, which ended without success last weekend.
Mr Brokenshire has invited parties to another round of talks on Monday.
The UK and Irish governments have said they want the talks at Stormont Castle to have an agreed agenda and regular roundtable meetings.
The two governments have described it as "an intensive process to drive progress".
The parties missed Monday's deadline for forming a power-sharing executive.
However, Mr Brokenshire said he believed there was still a window of opportunity for further dialogue.
Mr Brokenshire also told MPs earlier this week that he does not believe there is an appetite for a fresh snap election.
He said he does not want to see a return to direct rule from London, but has to keep all his options open.
Secretary of State James Brokenshire has said he does not see a role for an independent mediator or chair in the next round of Stormont talks.