The Reds are set to face Eddie Howe's men in the Saturday 12.30pm slot as a result of the game being selected for broadcast by BT Sport.
With the opening game of that double-header taking place on Wednesday, April 27, Liverpool's preparation time for their clash with the Magpies will be severely limited.
As such, they have asked the Premier League and BT Sport to consider moving that fixture to the rarely used Saturday evening slot.
That would see the Reds kick off at 7.45pm, allowing for an extra seven hours of recovery time following the first leg against Villarreal.
However, it is understood that senior figures at the club are not optimistic the request will be granted by the Premier League.
Klopp applied public pressure to both the league and BT Sport in his press conference on Thursday afternoon, calling for a 'common sense' approach.
📺 Jurgen Klopp on Newcastle after Villarreal:
"Playing at 12:30pm makes a massive difference. Every single hour counts, I don't understand it." 🔴 pic.twitter.com/A44o7shEN9
"If you want to cause us problems you send us to 12.30 at Newcastle," he said.
"I don’t understand it. I can understand that people want to see a football match between Liverpool and Newcastle but I don’t see why any team should have an advantage or a disadvantage.
"The league and the broadcaster really have to try at least to help. We will see. I haven’t heard anything yet. Nobody from BT contacted me yet.
"But I’d say common sense would tell you that it's probably the right thing to do to move the game slightly backwards."