Brokers at Barclays and Citigroup both estimate the supermarket will post a 1.1 per cent fall in like-for-like sales figures for the 12 weeks to June 7.
In the previous quarter Sainsbury's saw its like-for-like sales fall 3.1 per cent, but Barclays warns against reading too much into the recovery because of the impact of Easter and other one-off comparables.
Sainsbury's fourth quarter fall was the first in many years. However, the legacy that Mr King hands to commercial director Mike Coupe when he steps down next month following 10 years in charge is nine years of rising annual profits.
Analysts believe next week's figures will represent a good result for the business considering the price pressure on the big four supermarket retailers from German discounters such as Aldi and Lidl.
Citigroup said comparisons between the big four is becoming "a two-speed story" as the performance at both Asda and Sainsbury seems to have stabilised over the last two months. Asda saw its most recent like-for-likes edge up 0.1 per cent in the 15 weeks to April 20.
This is in contrast to Tesco and Morrisons who continued to lose market share over this period. Morrisons saw its first quarter like-for-likes fall 7.1 per cent in the 13 weeks to May 4, while this week Tesco posted a 3.7 per cent drop in underlying sales for the first quarter to May 24.
Investors expect the digital makeover of Argos to show more progress when parent group Home Retail reports its first quarter trading on Thursday.
In recent years Argos has refreshed its store formats and beefed up its multi-channel offer. Analysts at Barclays said the chain's "best in class" click-and-collect capability has transformed the large store portfolio.
Flybe is expected to show it has turned the corner after two years of losses when it posts its annual results on Wednesday.
The market expects the regional airline to report a full-year pre-tax profit of £6.7 million on sales of £621 million. This compares with the previous year's £23.2 million loss amid higher fuel costs and a declining domestic market.