The Reds have been linked with both players ahead of the January window as they supposedly look to further strengthen their attacking ranks.
Chiesa and Vlahovic were both on the field on Saturday when Juventus battled to a late 1-0 win over Fiorentina at the Allianz Stadium.
Calciomercato reports that Liverpool scouts were present in the stands, with Vlahovic - who is set to be sold by I Viola next year - said to be the main focus of their attention.
However, the Reds face intense competition for the Serbia international as domestic rivals Tottenham Hotspur, Arsenal, Manchester City have all been linked, as well as Juventus.
Vlahovic has already struck eight goals in 10 Serie A games this season after netting 21 times in the competition last term. body check tags ::