Coupe has been at Sainsbury's, Britain's No. 2 supermarket chain, since 2004 and group CEO since July 2014.
Though no timetable has been announced for his departure, he has faced questions about his future since April when Britain's competition regulator blocked Sainsbury's attempt to take over Walmart owned rival Asda for 7.3 billion pounds.
Coupe was the architect of that deal and Sainsbury's share price has fallen 20% over the last year. Like its big four supermarket rivals, including market leader Tesco and Morrisons, Sainsbury's is continuing to lose market share to German-owned discounters Aldi and Lidl.
Despite seeing his grand merger plans thwarted Sainsbury's shareholders overwhelmingly backed Coupe's reappointment in July and the following month, the group reiterated that Coupe had the board's full support. In September, he presented an updated strategy designed to show Sainsbury's could prosper on its own.
Coupe will turn 60 this year.
"Lots of things would point towards it (Coupe's departure) being this year," one of the people said.
"The annual general meeting (in July) would make the most logical last day."
Sainsbury's declined to comment.
Analysts had identified three internal candidates - Roberts, chief financial officer Kevin O'Byrne and food commercial director Paul Mills-Hicks - after the previous frontrunner, Argos boss John Rogers, quit in October to join advertising firm WPP.
Roberts has since emerged as the clear internal favourite, though good corporate governance dictates that Chairman Martin Scicluna would also conduct a thorough external search process, the people said.
Roberts joined Sainsbury's in July 2017 as central retail and operations director responsible for stores, central operation and logistics.
Before that he was executive vice president of Walgreens Boots Alliance and president of health and beauty retailer Boots. Prior to this Roberts was managing director of Boots UK, where he was responsible for leading retail and pharmacy activities in over 2,500 stores across the UK and Ireland.
Earlier in his career Roberts spent 14 years at Marks & Spencer, where he had roles in stores and operations.
If he does get the job it will mean Britain's two biggest supermarket groups - market leader Tesco and Sainsbury's - will be run by Boots alumni.
Ken Murphy, a former joint chief operating officer at Boots UK & Ireland, will succeed Dave Lewis as CEO of Tesco in the summer.
Sainsbury's updated on Christmas sales on Wednesday. Core sales slipped as a drop in demand for toys and gaming eclipsed a solid performance in food.
(Reporting by James Davey, editing by Louise Heavens)
By James Davey