Laurie McIlwee, who has been with the group for 14 years, is understood to be planning to hand in his resignation imminently following shareholder pressure and as speculation mounts over clashes with boss Mr Clarke over strategy.
Sources close to Mr McIlwee reportedly said he had lost confidence in Mr Clarke's turnaround plans, but rumours of his departure have also been circulating for some months after investors are said to have questioned the finance director's position following a larger-than-expected slump in central European profits last autumn.
It is felt he should have guided forecasts lower before the half-year results in October, which revealed a 71% plunge in European trading profits.
His departure would compound woes for Mr Clarke, who is already struggling to make a £1 billion overhaul bear fruit.
Mr Clarke recently unveiled plans for £200 million of price cuts and another 150 convenience stores to halt sliding UK sales after losing out to the likes of discounters Aldi and Lidl.
It is expected to report another set of disappointing results on April 16, with analysts predicting a 10% slump in profits.
This comes after it last year reported its first annual profits fall in nearly 20 years.
And sales have since failed to turn around in a difficult market - falling by 2.3% over Christmas, while discounters and premium retailer Waitrose fared far better.
Tesco was not immediately available for comment.
Independent retail analyst Nick Bubb said: "It is perhaps more than a little unfair that Tesco finance director Laurie Mcllwee is to be the scapegoat for Tesco's profit weakness, but his communications skills seem to have left him vulnerable."
Mr McIlwee's expected exit will raise further questions over the overhaul being led by Mr Clarke, whose own future at the group has been the subject of speculation.
He told retailers last month he was set to remain at Tesco for a "few years".
Mr Clarke's tenure has been fraught, with the group issuing its first profit warning in 20 years just a year after he took over from predecessor Sir Terry Leahy in March 2011.
Mr McIlwee has been group finance chief since January 2009, but started with the group as UK finance director in 2000 before being appointed distribution director four years later.