Le 10 Sport says Sanches is top of the list to replace Gini Wijnaldum. The Dutchman comes off contract in June.
The Portugal international shot to fame in 2016 when he was awarded the Golden Boy award with Benfica.
An ill-fated spell at Bayern Munich followed, where he was first introduced to English football through an equally-discouraging loan at Swansea.
But now at the age of 23, the midfielder looks to have ironed out those early frailties and is looking back to his best.
And he has continued that form into this season with Klopp liking the look of the Amadora-born star.