Grillitsch is a free agent following the expiry of his contract at Bundesliga club Hoffenheim and he has been linked with a host of Premier League sides.
The midfielder is still a free agent however and jury is out on where he will continue his career, but it will not be at Brighton.
Seagulls boss Graham Potter is a fan of what the Austria international can bring to the table and Brighton put an offer in front of him.
Talks were held with the player and his agents, but Brighton then withdrew the proposal.
It is claimed that they took their offer off the table due to doubts about Grillitsch’s personality.
The midfielder made just 18 appearances in the Bundesliga for Hoffenheim last season as injuries played their part.
Grillitsch made a total of 150 appearances for Hoffenheim during the course of his time at the German club.
