The Clarets sold Andre Gray to Watford on Wednesday, and there's a chance he could be replaced by the man whose void he was bought to fill two years ago.
Sky Bet had previously listed Burnley at 8/1 to bring Ings back to Turf Moor, with only linked club Newcastle deemed a more likely destination.
But after confirmation of Gray's departure, odds on Sean Dyche's side were cut to 11/2, moving them ahead of the 7/1 Magpies - though the England international is 2/7 to remain at Liverpool.
According to a report by The Sun last month, Newcastle could have difficulty landing Ings after their relationship with Liverpool was strained by United's attempt to sign Anfield youngster Sheyi Ojo - which could be music to Burnley's ears.
Ings scored 43 goals in 130 Clarets appearances, but has seen his Liverpool career been blighted by injuries.
Nevertheless, the 25-year-old, who recently returned from his second long-term lay-off, has still managed to score three goals in 11 Reds outings.
Newcastle, meanwhile, continue to hunt for a new striker, having also been linked with a move for Gray.
Could Burnley land Liverpool's Ings ahead of Newcastle?