Hamburg and Werder Bremen were both reported to be interested in the giant forward before Hoops boss Ronny Deila moved on transfer deadline day to make an offer.
But Braunschweig rejected the bid and the Parkhead side may now return in January in a fresh move.
The attacker said: “There was an offer for me in the last day of the transfer window, but out of respect for the club I won’t say who it was.”
That club was Celtic who were left disappointed in their failure to add to their squad.
Berggreen has netted four goals in eight starts for the German side this season and grabbed five goals in 13 during the last campaign after his move from Danish minnows Hobro.