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.
Andre Gray in action for Burnley (right)
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.
Danny Ings in action for Liverpool
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?