Cuadrado, 27, has been on loan at Juve since the summer after failing to earn a place in Jose Mourinho's first-team plans.
The Colombia international was expected to make his move to Turin permanent next month when the transfer window reopens.
But Italian newspaper Gazzetta dello Sport now claim those discussions will be pushed back until February.
It was claimed last week that Barcelona were keen on the player and that their interest could scupper Juve's hopes of making the move permanent.
Yet former Fiorentina ace Cuadrado, who has played 20 games for club and country this season, appears to have his heart set on remaining in Serie A.
"The idea of coming back to Italy attracted me a lot. I know the football here, I know the language and the people, and the truth is it feels like my second home," he told UEFA.com.
"So when I had to decide about whether to take this chance or not, I talked to my agent every day about my return and now I am very happy to be here at Juventus."