"Douglas Costa is currently undergoing a routine medical ahead of a proposed transfer from Bayern Munich," Juventus said on their website.
The Brazil international, capped 21 times, will join Juventus on a loan for a fee of 6 million euros, according to Italian media.
The contract should also envisage the option to make the move of the 26-year-old permanent for 40 million euros.
Costa spent five years at Ukrainian top-tier club Shakhtar Donetsk before joining the Bundesliga champions in 2015, making 23 league appearances last season and scoring four goals.