Grillitsch is out of contract at Hoffenheim in the summer and was linked with a potential exit from the Bundesliga outfit in the recently shut January transfer window.
He stayed put though and hired a new management agency in advance of a move in the summer as he will not extend his deal at Hoffenheim.
The 26-year-old has a growing number of suitors and, according to German magazine Kicker, Arsenal and Newcastle are amongst them.
Also eyeing Grillitsch are Serie A trio Roma, Lazio and Napoli.
The Austria international is able to sign a pre-contractual agreement with any of the five clubs now at all time until the expiration of his deal at Hoffenheim.
Both Arsenal and Newcastle are expected to be in the market for midfielders in the summer and either could welcome Grillitsch to the Premier League.
There remains time though for other clubs to join the hunt for the Hoffenheim midfielder.
