The Reds are looking for potential Philippe Coutinho replacements amid fears they could lose their battle to keep the player.
Coutinho wants out of Anfield and Barcelona could launch a third bid after seeing two offers turned down.
Insigne is said to be Liverpool’s No.1 choice to come in for the Brazilian.
He scored 20 goals for Serie A giants Napoli last term and Klopp is a big fan of the midfielder.
But he’ll turn to Meyer if the Italian doesn’t fancy a switch.
The 21-year-old has just a year left on his contract at Schalke and The People say he’s turned down a new offer.
And they add he’s open to moving to Liverpool and taking up the opportunity to work with Klopp.
Bayern Munich are also keen on Meyer.
Tottenham have also been tracking the youngster, who helped Germany win the Under-21 European Championships last summer.
