The Reds are keen to bring the Dutch international to Anfield with the midfielder hopeful of a return to Premier League football.
And Liverpool have now made a formal approach for Wijnaldum and are in the process of negotiating a deal, the Newcastle Chronicle report.
The report suggests the Magpies are holding out for a fee close to £27million but Liverpool are yet to meet that.
Rafa Benitez is keen to keep hold of the attacking-midfielder however and Liverpool are likely to have to up their offer if they want to secure him.
The Spaniard said last week when asked about Wijnaldum and Moussa Sissoko’s futures: “We want to keep them, so I will not talk about money.Â
Georginio Wijnaldum - 5 things you need to know
“We want the right balance and we will make the right decision for the club.
"He's [Wijnaldum] a professional. A very good player, which we know. He's training well, which is good for him and also for the team.
"I've had these situations in the past with players. Some can get disappointed, but we are a group of professionals and still they have to keep working."