It is believed that the attacker will be available for a transfer fee of just £12m this summer due to a release clause in his contract following Stoke City's relegation from the Premier League. "It's the best league with the best players, but I do not want to exclude anything".
Now, today, the Bleacher Report's Dean Jones claims that the Reds have met with Shaqiri's representatives for talks about signing the 26-year-old.
But speaking to Swiss outlet Blick Sport while on global duty with the national team, Shaqiri was asked about the rumours surrounding his future.
Switzerland are in a group with Brazil, Serbia and Costa Rica and kick off their campaign against the five-time winners on Sunday June 17.
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Speaking to reporters ahead of the game, he said: "We've gone over the Austria game thoroughly with the coaches and analysts". Pleasingly from a German perspective, captain Manuel Neuer kept a clean sheet in his 45-minute spell in goal.
And any deal for Shaqiri is not dependent on Liverpool sealing the transfer of Nabil Fekir from Lyon.
The 26-year-old is now on worldwide duty with Switzerland ahead of the World Cup and he's apparently eager to find a new club before the tournament starts.
Shaqiri featured as Switzerland won their final pre-tournament friendly against Japan, running out 2-0 winners, and the former Bayern star was asked about the possibility of a move to Liverpool following the game.
"I am focusing on the national team right now".