Borowski, believed to be on Martin O'Neill's summer shopping list, has been told he is surplus to requirements at Bayern Munich just a year after joining on a free transfer from Bremen.
And director of sport Allofs says the 29-year-old is an option they are seriously looking at after confirming he had "discussed things" with the former Germany international.
"If the financial side of things is right, and we are convinced that signing him back would make sense for our squad, then we will deal with it," added Allofs in the Kreiszeitung Syke newspaper. "It is no secret that we are still looking for one or two additions and Tim could be a solution."
Borowski is due to return to Munich on Wednesday where he has already been told that he does not figure in the plans of new coach Louis van Gaal.
Of Bremen's interest, the defender said: "It's very interesting. We'll have to see how things develop."