Goal reported last week that the Bianconeri have offered €10 million to land Costa on an initial loan deal with an obligation to buy him permanently for €30m at the end of next season and the two sides were close to an agreement. The Serie A side have already agreed terms with the attacker worth €6m per season.
And Bayern CEO Karl-Heinz Rummenigge has confirmed Costa has made it clear he wants to leave Bayern, who are willing to sell if their asking price is met.
"We are in talks with Juventus, but there is no signed deal yet," Rummenigge said at the presentation of close-season signing Corentin Tolisso.
"The player told us that he would like to leave the club. I won't lie, there is an amount, and when this amount will be paid, we are ready to finalise the deal. The talks are positive and serious."
Rummenigge also suggested Bayern were open to loaning out Renato Sanches after the Portugal international only started six Bundesliga matches last season following his big-money move from Benfica, as well as recent signing Serge Gnabry, who has been linked with Hoffenheim.
"His first year was not easy and not satisfactory for either party," said Rummenigge of Sanches.
"It is incredibly important that he plays on a regular basis. We'll think about whether it would be better to loan him."
On Gnabry, he added: "The player and his agents communicated that they would prefer a loan for one year.
"We are staying calm and we will see what happens in the transfer market."