Sky News has learnt that IHG, which has a market value of just over £9bn, is working with headhunters on a search for Mr Cescau's replacement.
City sources said on Monday said a successor to Mr Cescau, who joined the IHG board in 2013, was likely to be in place by the time of next year's annual meeting.
Mr Cescau is one of the most prominent figures in British boardrooms, having served as chief executive of Unilever and as a director of companies including Pearson, Tesco and British Airways' parent, International Airlines Group.
Shares in IHG have begun to recover after being badly dented by the COVID-19 crisis, with the company's stock up 14% during the last year.
In August, it announced plans to launch an upmarket leisure hotels brand as it seeks to capitalise on recovering consumer demand for foreign holidays.
Keith Barr, the company's chief executive, said that trading had improved markedly during the first half of the financial year, "with travel demand returning strongly as vaccines roll out, restrictions ease, and economic activity rebuilds".
He added that the recovery had been most pronounced in Greater China, where IHG has a big presence.
Last month, the company named Joanna Kurowska as the new head of its business in the UK and Ireland.
IHG declined to comment on the search for a new chairman.