Ronny Deila failed to bring the Danish striker to Parkhead in the summer, but may try again next month.
The Bhoys had a £2.25m bid for the 22-year-old turned down on the final day of the summer window (claim the Record), but Ronny Deila is clearly hoping that he can still him prise him away from the German club.
The Denmark under-21 international has been in decent form for the second division side this season. He has four goals from 12 league appearances to help Braunschweig to sixth place in the table. While Freiburg and Leipzig have already moved six points clear of their nearest rivals at the top, St Pauli - who currently occupy third, and the promotion play-off spot - are just four points ahead of Berggreen's side.
The Daily Record suggest, however, that Werder Bremen and Hamburg are also interested, and with Berggreen's growing knowledge of the German game, he may decide that stepping up to the Bundesliga may be the best decision for him.
But with Celtic four points clear at the top of the Scottish Premiership - and with a game in hand over Aberdeen - a move to Glasgow would certainly present Berggreen with his best opportunity to play in the Champions League.