Cuadrado was sent on loan to Juve before the start of the season after a torrid debut six months at Chelsea.
He arrived from Fiorentina in a £27million switch that also saw Mo Salah head the other way in February 2015.
It is added that the situation could be complicated by Antonio Conte's impending arrival at Stamford Bridge.
Italy head coach Conte is supposedly an admirer of Cuadrado and there are suggestions the Colombia international could seek to revitalise his Blues career under the new boss.
Juan Cuadrado - Spotlight on
Express Sport understands Conte, 46, will be appointed Chelsea boss once his quits the Italy post after Euro 2016.
But Juve hope they can secure Cuadrado before Conte is installed.
The 27-year-old has made 33 appearances for Juve this season and scored in their 4-2 Champions League defeat at Bayern Munich on Wednesday.
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