And Alaba would slot straight into Liverpool’s team with Klopp failing to replace Dejan Lovren last summer.
Fabinho is currently the only senior centre-back available to Klopp currently with Joel Matip, Joe Gomez and Virgil van Dijk out injured.
Matip is expected to return at the end of the month, but both Gomez and Van Dijk face length spells on the treatment table.
Liverpool’s injury crisis has led to calls for the club to bring in central defensive cover this month.
But reports have suggested that transfer chief Michael Edwards is focussing more on deals for the summer.