The Italian outlet states that the Juve president Giuseppe Marotta will make another offer for the Germany international.
Gundogan worked alongside Liverpool boss Jurgen Klopp at Dortmund for several seasons before Klopp left at the end of last season.
The Germany international admitted earlier this week week that he was considering his future.
“There is still no decision, and of course, everything has to be considered very carefully, because your career is limited in time,” Gundogan was quoted as saying by Goal.
“But to be honest, everything is still open.”
Gundogan has been linked with a move to Anfield since the appointment of Klopp as manager in place of Brendan Rodgers.
Gundogan is tied into a contract at Dortmund until 2017 after signing a contract extension at the start of the season.