The high-profile BBC figure is in talks to step down as political editor after six years and switch to presenting the Today programme, it has been reported.
Jon Sopel, currently the corporation’s North America editor, is said to be leading the field of internal candidates to replace Ms Kuenssberg at Westminster.
But MP Julian Knight, chair of the Digital, Culture, Media and Sport committee, said the corporation should “throw the net wider” and find a Brexiteer to find a replacement if there is a vacancy in the key position.
“This would be an opportunity for the BBC, maybe, to look at journalists who had a much more pro-Brexit [approach],” the influential Tory told The Telegraph.
Mr Knight added: “In front of our committee [BBC director general] Tim Davie could not name any senior person he had employed during his watch who supported Brexit. Maybe this is a chance to correct that.”
The senior MP recently attacked the BBC for not “getting on with it” after the Brexit referendum, saying: “It was not in touch at all over Brexit – it had a collective nervous breakdown in my view.”
The media select committee chair did offer praise for Ms Kuenssberg’s work, however, saying that she “will be a really sad loss to the role, she brings real insight”.
His call for a pro-Brexit political editor follows Tory concern about the appointment of Jess Brammar to a senior role in BBC News, despite an impartiality row over her old tweets.
Some right-wing media outlets drew attention to Ms Brammar’s now-deleted tweets, which were critical of Brexit. BBC board member Sir Robbie Gibb – former communications director to Theresa May – reportedly objected to her appointment.
After weeks of sniping from Conservative MPs, the former editor of HuffPost UK was given the job of overseeing the BBC’s domestic and international news channels in September.
The BBC has not been drawn on reports about Ms Kuenssberg was switching roles, but has confirmed that Mr Sopel would be leaving his current job and returning to the UK.
A note seen by The Independent, from head of news Jonathan Munro to staff earlier this week, read: “He will wrap up in Washington at the end of November, then take a career break to catch up with family now dotted around the globe, before returning to a role in the BBC next year.”