The Deputy Speaker and Labour MP has been gearing up for the role since Mr Bercow dramatically announced his intention to quit the chair on October 31.
He has consistently remained in poll position to take the chair, with key book makers setting the odds of his victory at a comfortable 4/7.
Ladbrokes, Betfred, Coral and Betway all agree on these 4/7 odds, with William Hill listing him at 8/15, PaddyPower at 8/13 and bet365 at 1/2.
Sir Lindsay, 62, has been the Labour MP for Chorley since 1997 and Deputy Speaker since 2010.
Although he is firmly rooted in his Lancashire constituency, which supported Leave in the 2016 referendum, he has never declared his views on Brexit.
On his tail is Mother of the House Harriet Harman, whose odd stands at 3/1 across Ladbrokes, Coral and Betfred.
Ms Harman, 69, has represented Peckham (later Camberwell and Peckham) since 1982 and is one of the most prominent figures from Tony Blair’s New Labour era.
She has pledged that she would remain neutral in the chair, telling the BBC: “Once you offer yourself for election as Speaker, you are making a promise you will set (your party) aside and be neutral, so whoever (is Speaker) will have to go through that transition.”
She has defiantly pressed ahead with her campaign, despite recent threats from her local party to derail it.
Ladbrokes list both rivals neck-and-neck at 10/1, while bet365 and betway favour Dame Eleanor and Paddypower favours Mr Bryant.
Dame Eleanor, 61, is one of Mr Bercow’s three deputies, alongside Sir Lindsay and Labour’s Dame Rosie Winterton.
She has insisted the Speaker’s successor must be an "independent anchor... unaffected by an allegiance to any political objective".
Her close rival for the role Mr Bryant, 57, is a high-profile Labour candidate, having served as a junior minister in the last Labour government.
The MP for Rhondda has also served as shadow culture secretary and shadow Commons leader, and now chairs the Commons finance select committee.
Mr Bercow announced his plans to stand down as Speaker on Monday, September 9, adding that he would also quit as an MP.
He said he would wait until October 31 to leave the post, to ensure the Commons had the guidance of an “experienced figure" in the run-up to Boris Johnson’s avowed Brexit deadline.
However, he also confirmed he would step down earlier if a sudden early general election were called.
Having served in the role since 2009, the outgoing Speaker described it as “the greatest privilege and honour of my professional life.”
Among the outsiders hoping to fill his shoes are Procedure Committee chair Charles Walker, fellow Deputy Speaker Rosie Winterton and, one of the first to throw his hat into the ring, Sir Edward Leigh.