The 20-year-old right-back is out of contract at Lechia Gdansk and the Light Blues are nearing an agreement to sign him.
Reports in Poland claim Zukowski is likely to put pen to paper today with the player expected at Ibrox to finalise talks and thrash out terms in a £500,000 deal.
Manager Giovanni van Bronckhorst has been eyeing cover for captain James Tavernier following the departure of Nathan Patterson to Everton at the beginning of the month.
The Scottish champions look to have beaten competition from Legia Warsaw to land the Poland Under-21 international.
Zukowski came through the youth ranks at Lechia Gdansk and made his senior debut in 2017. He has gone on to make 60 first-team appearances, establishing himself as a key player this season.
He will become Rangers THIRD January addition after the loan arrivals of James Sands from New York City and Amad Diallo from Manchester United.
Meanwhile, Rangers goalkeeper Jon McLaughlin has signed a new contract until the summer of 2024.
The 34-year-old Scotland international joined the Gers in 2020 and has provided back-up to veteran shot-stopper Allan McGregor.
McLaughlin has made 24 first-team appearances to date, keeping an impressive 17 clean sheets.
Speaking after penning his new deal, McLaughlin said: “I am delighted to have committed my future to Rangers for the next two-and-a-half years.
“I have thoroughly enjoyed my time at the club so far, and being a part of the team which won the title last season will live with me forever.
“I want the opportunity to be a part of future success at this club, while hopefully also adding more Scotland caps to what I have already.”
Goalkeeping coach, Colin Stewart, continued: “This is great news for Jon and for the club.
“He has added so much to the department both on and off the field in his time here so far and I look forward to working even more with him in the coming years.”
Sporting Director, Ross Wilson added: “I am delighted Jon has committed his future to Rangers.
“Since he joined the club, he has been a fantastic professional both on and off the pitch, while his performance levels on all occasions have been strong.”