Serie A rivals Inter Milan also remain interested in the Brazil international, who was omitted from Brendan Rodgers' match-day squad for last weekend's game against Stoke following a fall-out.
Inter's interest dates back to January when coach Roberto Mancini first tried to sign him, but Juventus are also now monitoring the situation.
Juve recruited Sami Khedira on a free transfer from Real Madrid in the summer, but the injury-plagued Germany international faces being out until October after picking up a thigh injury.
The last time Khedira made more than 20 starts in a domestic campaign was for Stuttgart in 2009-10 and, while Draxler is high on their wanted list, Lucas has also come under scrutiny.
Liverpool still hope Mario Balotelli will leave before the transfer window closes - Sampdoria retain an interest - while striker Fabio Borini is also surplus to requirements.
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