The Hungarians, who have been paired with Shamrock Rovers in the qualifying rounds in each of the last two seasons, are in this term's Europa League, where they will play AZ Alkmaar in a fortnight. Without a manager after Pascal Jansen joined MLS side New York City, they are second in their domestic league.
The Tallaght native spent 18 months as boss of Maccabi Tel Aviv before leaving the infamous role in Israel last June. Keane led the team to the last 16 of the Europa Conference League, won a league title, and claimed the Toto Cup during his spell in charge of the Israeli club.
Keane has also had spells with the Republic of Ireland, Middlesbrough, and Leeds United.
Gábor Kubatov, the president of the FTC, admitted in a video uploaded to his official social media pages that the football team has a new head coach but did not name Keane as the next boss.
"So the question is, do we have a new coach? We do. Announcement coming soon. Come on, Fradi!" said Kubatov.