The 24-year-old is currently in his third campaign at the Bundesliga outfit, making a total of 78 starts and 11 substitute outings during his time at the club.
However, the Austria international has been linked with a move to the Premier League in recent months, and it appears that offers will be made later in 2020.
According to Bild, Arsenal are contemplating an approach for the player as Mikel Arteta looks to strengthen his options in the centre of the pitch.
Grillitsch has a contract at Hoffenheim until the end of the 2021-22 season. body check tags ::