The 22-year-old goalkeeper, who has a year remaining on his contract at the Esprit Arena, is believed to be on the radar of a number of clubs, including Everton and Bundesliga side Schalke.
The Germany Under-21 international, a summer arrival at Dusseldorf from Bayer Leverkusen last year, has produced a string of impressive displays for the Rhine club this season.
Former Bundesliga top scorer Allofs, who is on the club's board, says any interested suitors would have to offer at least €5m (£4.2m) to pique Fortuna's interest.
He told the Rheinische Post newspaper: "If there is any serious interest in Fabian Giefer, any starting bid would need to be beyond €5m. Otherwise this is nothing of our concern.
"In the end we would always have to insist there is still a valid deal existing between Fabian Giefer and Fortuna Dusseldorf."