Nathan Patterson departed the Gers earlier this month for Everton, thereby leaving the Ibrox outfit short in the right-back department.
The Gers are thus in the market for a right-back to add depth in that area and they have identified Zukowski as a suitable option.
Zukowksi currently plies his trade for Ekstraklasa side Lechia Gdansk, but he is set for a move in the closing hours of the window.
The right-back is currently in Glasgow and the pieces are falling into place to make him a Rangers player before the end of the day.
Upon his arrival at Ibrox, Zukowksi will provide competition to first-choice right-back James Tavernier, effectively replacing Patterson.
Zukowski is an academy product of the Polish side and the young right-back has enjoyed a breakthrough season for Lechia Gdansk.
He has made 18 appearances this season for the Polish outfit, becoming their first-choice right-back, and has also chipped in with two goals and one assist.