The Colombia international is widely expected to leave the Bernabeu during this summer’s transfer window, having found it difficult to contribute this season after returning from a two-year loan spell at Bayern Munich.
A number of clubs, including Arsenal, Everton, Wolverhampton Wanderers and Manchester United, have been credited with an interest in the 28-year-old.
However, according to reports in Spain, Juve are firmly in the hunt for the South American, who could allegedly be available for a figure in the region of €40m (£35m) ahead of the 2020-21 campaign.
Old Lady boss Maurizio Sarri is said to view Rodriguez as the perfect player to provide extra support for Cristiano Ronaldo in the final third of the field.
The playmaker’s current deal at the Bernabeu is due to expire next summer.