Mr Corbyn, who led the party to a humiliating defeat in 2019, is viewed as the ideal option to lead the opposition should the incumbent leave. A DeltaPoll poll released over the weekend shows him tied with Yvette Cooper.
The pollsters surveyed Britons in seats won by the Tories in 2019.
It found Mr Corbyn and Ms Cooper tied for the top option to succeed Sir Keir, with 8% each.
Ed Miliband came second with 7%, while only 4% preferred Angela Rayner for the top post.
The findings came despite Mr Corbyn being frequently mentioned as a factor for the Red Wall seats' poor performance in December 2019.
Labour gained 203 seats, down 59 from 2017, in its lowest night since 1935.
Boris Johnson gained an 80-seat majority when Labour strongholds in the north and midlands refused to back Mr Corbyn.
Despite his backing, Mr Corbyn is now ineligible to run.
Sir Keir dismissed him as a Labour MP after he made anti-Semitic remarks following the publication of an investigation.
Following the election, Mr Johnson held a solid advantage over Labour in seats and nationally, although polling trends have reversed since.
Price increases, sleaze allegations, and suspicions the Conservative Government did not follow its own Covid lockdown regulations have all harmed the party.
DeltaPoll gives Labour a five-point lead over the Conservatives at 40% to 35%.
In the Red Wall seats, Labour would get 49% of the vote, while the Tories would get 33%.
Deltapoll co-founder and CEO Joe Twyman told the Sunday Mail: "The Conservatives' victory in 2019 was aided by winning over voters in previously unwinnable areas.
"Boris Johnson will have to work hard to hang onto the seats he acquired in 2019.
In light of recent incidents and a lot of pressing challenges, the Prime Minister may not have a happy new year.
While resentment at the incumbent government has increased support for Labour, the public appears unimpressed with Sir Keir's leadership.
With regards to Yvette Cooper, the MP for Holborn and St Pancras has a net score of six.
From December 23 to 30, DeltaPoll polled 1,567 adults.