The Bhoys have snapped up four players this summer, bringing in Logan Bailly, Saidy Janko, Dedryck Boyata and Nadir Ciftci - but it seems that Ronny Deila hasn't done strengthening just yet.
The Scottish Sun report that Deila is now increasingly worried about Emilio Izaguirre's poor form at left back having struggled against Stjarnan in the Champions League last week, and could now look to bring in a new signing to solve the problem.
Charlie Mulgrew started at left back against Eibar on Saturday, but it appears that Deila wants a long-term option - with one specific target in mind.
St. Pauli defender Halstenberg, previously of Borussia Dortmund, is allegedly Celtic's top target this summer, with the 23-year-old seen as competition for Izaguirre after the Bhoys missed out on Mitchell Dijks, who joined Ajax.
However, Halstenberg was recently quoted by the Daily Express as saying that he intended to stay at St. Pauli until the expiration of his contract next summer - which could make a deal difficult for Celtic.
How much of a concern is Izaguirre's poor form?
Celtic have competition for places across defence, but Honduran international Izaguirre has been the undisputed first choice for the Bhoys for some time now.
Mulgrew offers a versatile alternative given that he can also play at centre back and in defensive midfield, but Deila will understandably want a natural left back to come and compete with Izaguirre.
Izaguirre's drop in form may be down to the lack of quality competition for his role - and Deila is right to be looking at potential signing to push the Bhoys ace next season.