Though Benitez made seven signings during the off-season he missed out on a number of key targets, including Tammy Abraham, Willy Caballero and Kenedy.
The Toon have won three of their seven Premier League games this season to occupy an early position in the top half, but have netted just seven times. New signing Joselu is their top scorer with just two.
But according to the Shields Gazette, Newcastle will attempt to convince Liverpool to part ways with Ings on either a permanent or loan deal.
The England forward has endured a nightmare spell at Liverpool since joining from Burnley in the summer of 2015. Back-to-back knee injuries have restricted the 25-year-old to just 12 appearances in 27 months for the Reds.
During that period the club have added Roberto Firmino, Sadio Mane, Mohamed Salah and Dominic Solanke to their attack. Daniel Sturridge also remains, meaning Ings has plummeted down the pecking order, leaving his Liverpool future looking discernibly bleak.
A loan move to Newcastle would allow Ings the chance to prove his fitness to Klopp – he has made just one outing this season as a substitute in the Carabao Cup defeat to Leicester City – with the Winchester-born hitman still keen on carving out a career for himself at Liverpool.
"Everywhere I have been, I have always found a way to make it happen. I have been in a lot of tough situations at previous clubs where it has been hard to break in," Ings told The Times. "People from the outside looking in will probably have the assumption, 'Oh, he's the forgotten man' but it has not crossed my mind at all. I still believe in myself. I still believe I can play in this team.
"When you are at a club like Liverpool, it is not a club that you want to walk away from. It would grate on me for the rest of my career, and the rest of my life, if I had not done everything to give it my all. I still feel like I have a big part to play in this football club."
Benitez's desire to further improve his attack is well-known after Newcastle missed out on the deadline day acquisition of Lucas Perez. The Spaniard eventually chose to return to Deportivo La Coruna after a nightmare first season with Arsenal, a move that thwarted Dwight Gayle's proposed move from St James' Park to Championship side Fulham.