The announcement will illustrate the ongoing squeeze on Britain's established supermarkets.
The latest industry figures showed that Britain's biggest grocer saw its market share fall to 28.6% in the 12 weeks to March 31, from 29.7% a year earlier. Discounters Aldi and Lidl have been picking up market share at the expense of the established grocers.
Analysts expect underlying pre-tax profits at Tesco to fall by 15% to around £3 billion for the year.
Mr Clarke is in the middle of a £1bn turnaround plan launched after it posted its first fall in group profits in nearly two decades last year.
Among those favoured by investors as replacements are thought to be former Dixons chief executive John Browett and the head of Unilever's personal care business, Dave Lewis.
Mr Browett currently runs fashion chain Monsoon Accesorize but used to run Tesco's online business.
As president of personal care at Unilever, Mr Lewis looks after huge brands include Dove soap and Persil washing powder.
Other names being mentioned are former Tesco executives Tim Mason and David Potts.
Some investors have also suggested that chairman Sir Richard Broadbent could be replaced.
Figures published today by Barclaycard illustrate the pressure on middle-market retailers. It reported a 21% rise in consumer spending in discount stores, budget grocers and fashion outlets over the last 12 months.
Tesco has been retrenching from loss-making international businesses to focus recovery efforts on the UK, where it is scrapping more than 100 major store developments and focusing on convenience and online retail.
Last week, it emerged finance director Laurie McIlwee is to step down amid reports he had lost faith in the group's strategy.
Tesco's latest trading update revealed sales fell by 2.4% over the festive period, while Hargreaves Lansdown analyst Keith Bowman said a 2% decline was expected for the fourth quarter to February.
He added there would be close attention on whether Tesco upped its price-cutting strategy, to which it has pledged £200 million.
Mr Bowman said: "An aggressive change of strategy continues to be considered by analysts."
City analyst Pradeep Patel said: "If Tesco were to match Morrisons' cuts we think it would have to invest an additional £500m in prices this year."
l Debenhams publishes half-year results on Tuesday months after issuing a stark profits warning when a hoped-for surge in Christmas sales failed to materialise.
Margins were lower partly because the department store cut prices to compete with a wave of high-street promotions, but these failed to entice the numbers, with like-for-like sales rising by only 0.1% in the 17 weeks to December 28, which forced more reductions to clear stock in the new year.
Pre-tax profits are now expected to slump by 29% to £85m when interim results are announced.
l On Wednesday, FTSE 100 house-builder Persimmon updates the City on its performance amid sector jitters that have put pressure on shares.
There has been speculation lenders are planning to rein in mortgage approvals due to fears of a housing bubble.