The 25-year-old could be a strong asset in the left-back position, which Ronny Deila is looking to strengthen ahead of the Champions League qualifying matches.
It is thought that Douglas would be available for £500,000 two years after leaving Tannadice and Deila has watched him for the Polish side as well as the Celtic scouting network keeping tabs on him since departing Dundee for Poland.
Douglas is believed to be open to a move if Lech Poznan miss out on Champions League football and they are currently embroiled in a three-way fight with Leiga Warsaw – who they beat at the beginning of May – and Jagiellonia Bialystok who beat them 3-1 on Sunday.
Poznan are in no rush to sell Douglas after his one-year contract extension was triggered by playing in more than 50 per cent of their games, but Celtic will have to act quickly as there is said to be interest from Russia and Germany.
The 25-year-old has featured 23 times for the Polish outfit this season, finding the back of the net three times – including the opener in the recent win against Leiga Warsaw – and has been booked on seven occasions with no red cards.