Pro-Leave Labour MP Kate Hoey is to run off against former shadow foreign secretary Hilary Benn today to lead the Commons watchdog on Brexit amid warnings the panel could be left "toothless".
Ms Hoey and Mr Benn - who was sacked by Jeremy Corbyn for disloyalty - have been nominated to chair the Exiting the EU Committee.
But the Institute for Government (IfG) warned that the size of the Brexit committee could hamper its ability to question witnesses and claimed that there were already too many competing parliamentary inquiries into the process of leaving the European Union.
MPs will vote later on who will chair the committee, which will scrutinise the work of David Davis' Brexit department.
The committee will be made up of 21 MPs, including 10 Tories and MPs from six opposition parties, while the average committee has 11 members.
The IfG warned it "risks being a large and toothless watchdog" with its size leading to "scatter gun" questioning of witnesses.
The number of MPs involved would also make it hard to ensure the same people turn up to every session and it could be difficult for the committee to achieve consensus.
The IfG suggested that the panel could attempt to get around Theresa May's reluctance to publicly discuss her Brexit plans by holding private meetings with ministers or asking for access to sensitive documents.
The proposal could see the Brexit committee follow the example of the Intelligence and Security Committee which issues "heavily vetted" reports, the IfG said.
In a report the think-tank called for better co-ordination between the various parliamentary committees examining Brexit, which have seen 31 inquiries launched by 24 different committees across the Commons and Lords.
It suggested the Liaison Committee could play a role in managing the process.
The IfG's Hannah White, who wrote the report, said: "Select committee scrutiny of Brexit risks becoming a chaotic competition for the limelight, diverting huge amounts of ministerial and official time which might have been better spent elsewhere.
"The MPs who sit on these committees - and the new chairs being newly elected on Wednesday - face a huge task undertaking scrutiny of Brexit. But they must rise to the challenge, because ultimately better scrutiny will mean better Brexit."
Leadership of the Brexit panel is one of two vacant select committee chairs allocated to Labour.
Leading Labour moderates Yvette Cooper, Chuka Umunna and Caroline Flint, along with veteran leftwinger Paul Flynn will contest the chair of the influential Home Affairs Committee - Labour's other allocated committee.
On the Conservative side, former sports minister Helen Grant is standing to chair the Culture, Media and Sport Committee against the committee's current acting chair, Damian Collins.
Tories Victoria Borwick, Stephen Metcalfe, Dan Poulter, Derek Thomas and Matt Warman are contesting the Science and Technology Committee.
Angus MacNeil is the only nominee for the SNP's allocated committee - International Trade.
Elections for the four contested positions will be held in the Commons with the results to be announced in the chamber.