Rangers have accepted an offer from Ajax for Calvin Bassey, with a deal worth in excess of £20m expected to be completed in the coming days.
It is also believed the Ibrox club have agreed a sell-on fee of 10% should the defender leave for Amsterdam.
The 22-year-old Nigeria international joined Rangers from Leicester City in 2020 and emerged as a key player last season.
Bassey was absent as Rangers beat hosts Blackpool in Saturday’s friendly match.
Speaking after the 2-1 victory at Bloomfield Road, Van Bronckhorst told Sky Sports: “It looks like Calvin is moving on. Of course I want to keep him. I’m really happy with his performances.
“In the end, everything we do it has to be in the best interests of the club. We have to look for another player to add to our squad. We have our list ready.”
Borna Barisic started in Bassey’s left-back role and scored the opener against Blackpool, with Charlie McCann netting the clincher.
James Sands started at left centre-back, where Bassey also played last season during Rangers’ run to the Europa League final and successful Scottish Cup campaign.
So far in the summer transfer window, Rangers have signed attacking players Antonio Colak, Tom Lawrence, Rabbi Matondo and Malik Tillman, with defender John Souttar having agreed a pre-contract move earlier in the year.