The UK's biggest supermarket chain is said to be choosing between Sir Ian Cheshire, who recently left home improvement retailer Kingfisher, and John Allan, the chairman of house-builder Barratt Developments.
However, the deal is far from finalised, and another City titan could still emerge as a possible contender, Sky News said citing a person close to the process.
Sir Richard Broadbent announced he would step down as chairman last autumn, following revelations that the supermarket misstated profits to the tune of £263m, rather than the initial £250m.
Whoever becomes chairman will help new chief executive Dave Lewis kickstart Tesco's recovery plan, unveiled in trading update earlier this year, which includes a new pricing strategy, plans to sell off parts of the business and an number of store closures.
Investors initially cheered the news but subsequent reaction has been mixed, with credit ratings Standards & Poor and Moody's slashing Tesco's rating to junk. At the same time, it's received an upgrade from broker Morgan Stanley, who felt the retailer's ability to improve its profit margins was being underestimated.
Earlier this week former chief executive Sir Terry Leah, who built Tesco into the high street giant it is today, blamed his successor Philip Clarke for the retailers troubles. He said it was a failure of leadership rather than the business or its employees.