The Reds have been linked with a move for the Ajax's attacking midfielder after a move for Nabil Fekir fell through earlier this month.
Morocco international Ziyech, who played in their opening World Cup match – a 1-0 defeat to Iran – has netted 19 goals over the past two seasons for his Dutch club, but concerns over his consistency remain.
The 25-year-old has also emerged as a potential transfer target for Serie A side Roma but their legendary striker Roberto Pruzzo – who plundered 106 goals in 240 games over a decade long spell between 1978-88 for the club – believes there are significant question marks over Ziyech's talents.