And it is said that Liverpool have started talks with Stoke over a deal for Shaqiri.
The Reds are aware they need more firepower if they are to challenge the likes of Manchester City, United and Tottenham for the Premier League title next term.
Their reliance on Mohamed Salah became evident last term - particularly when the player hobbled off in their Champions League final defeat to Real Madrid.
And Transfermarketweb say Liverpool are determined to beat United to his signature.
The 26-year-old has admitted he wants to stay in England.
Liverpool transfer news: Manchester United also want Xherdan Shaqiri (Image: GETTY)
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Shaqiri: "I'm not a fan" says Neville before World Cup clash
Speaking after Switzerland’s World Cup exit to Sweden earlier this month, he said: "At the moment, I can’t say anything.
"You’re going to hear soon on my future.
"I was not thinking about this because I was just focused on my national team and I wanted to make a good tournament for my team and my nation.
"It’s pretty normal to be aware of clubs being interested. Of course, I would like to play on the biggest stage in football, everybody knows that.
"I hope I can stay in the Premier League. I hope so, but you never know with football. I don’t rule out anything.”