Bhoys boss Tony Mowbray is keen to bolster his squad for the second half of the season and he is thought to be ready to firm up his interest in Stilic by making a bid for his services.
The 22-year-old has admitted he would be interested in a move to Celtic and expects talks between the two clubs to get underway this week.
"Celtic have been watching me for a long time. Scouts of the Glasgow side were at many Lech Poznan games and I guess they were satisfied with what they saw," Stilic told Sportin.
"On Friday I'm back in Poland and on Sunday Lech Poznan officials should start talking with Celtic.
"Of course I would be very happy to move to such a great club. But it is not up to me, Lech Poznan has to say yes to an offer they will receive from Scotland.
"It would be an honour for me to play for Celtic, but on the other hand I wouldn't be too sad if I would still be a Lech Poznan player after the winter transfer window."