The Whites are listed as joint favourites along with Newcastle United for the forward, both priced at 8/1.
Ings' former club Burnley had previously been favoured to sign the striker, but their price has now faded from 11/2 to 12/1 after they signed Leeds forward Chris Wood.
Celtic were previously 7/1 but have since dropped back to 10/1.
Liverpool signed Ings in 2015 but after a promising start at Anfield he suffered a cruciate knee ligament injury.
Then after battling back to fitness, Ings went down again with another serious knee injury, a cruel mental blow as well as a physical one.
The striker has now regained fitness and featured for the Reds in an under-23 game against Sunderland yesterday.
He is a player Liverpool boss Jurgen Klopp admires, but he must first prove his fitness.
A loan away from the club could be best if it guarantees him playing time, and Ings has experience in the Championship which could serve him well at Leeds.
He may however be more tempted to remain in the Premier League, whether that be at Liverpool or with a Newcastle side who are in need of extra firepower.