The 25-year-old Swedish striker, the son of Parkhead legend Henrik, is available on a free transfer after his contract terminated with Russian outfit Spartak Moscow was terminated by mutual consent.
The player's agent is reported to have contacted Celtic regarding the possibility of a move to Glasgow's east end, where his father is worshipped for his 242-goal haul across a seven year-spell that ended in 2004.
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Hide AdLarsson was also offered to Nottingham Forest but, according to Sky Sports, a move to the Bundesliga could now be on the cards, with the forward set to fly to Germany for talks with Schalke on Friday.
Wages and length of contract are a potential stumbling block though, with the two parties believed to still be some distance apart, but Celtic would appear to remain an unlikely destination despite the emotional pull.