The Dutchman has already added Antonio Colak, Rabbi Matondo and Tom Lawrence to his attack, and bolstered the defence with the arrivals of John Souttar, Ben Davies and Ridvan Yilmaz.
The loan acquisition of Malik Tillman from Bayern Munich makes it seven summer additions, and while the Rangers boss is happy with the squad at his disposal, he has not ruled out further incomings.
"There is still a couple of days. You never know what is happening in those days and you have to be prepared," he said after Tuesday night's 3-1 win over Queen of the South in the Premier Sports Cup.
A lot could depend on whether there are any departures from Ibrox.
Niko Katic has already gone - the Croatian defender joining FC Zurich for an undisclosed fee on Wednesday - with Mateusz Zukowski moving to Lech Poznan on loan, and more could follow out the exit door on deadline day.
The future of Alfredo Morelos remains uncertain with the striker having been banished from the first-team squad following his red card against Hibs due to concerns over his motivation and fitness.
Van Bronckhorst has been pleased with the Colombian's reaction, detecting a "change in attitude" as he prepares to welcome him back into the fold, but given Morelos is in the final year of his contract, today may be the day that Rangers decide to cash their chips if a suitable offer is made for the 26-year-old, with reports in Turkey claiming his agent has held talks with Fenerbahce.
Ryan Kent is another first-team star who is out of contract next summer. He has been linked with a move to Leeds United across several windows with no firm offer surfacing. It would be a surprise if he were to depart now with his debut in the Champions League group stages on the horizon.
Glen Kamara is also attracting interest with reports suggesting French side Nice could be preparing a £10million move for the Finnish international who cost Rangers just £50,000 from Dundee in 2019.
Another possible departure is Fashion Sakala. The Zambian striker has fallen out of favour this season, his only start coming against Queen of the South this week, and teams abroad are said to be sniffing around the 25-year-old.
Midfielder Stephen Kelly is lined up for a potential loan move with Livingston reportedly interested in signing the 22-year-old who spent the second half of last season at Salford City.
Rangers sprung one of the biggest surprises of the last transfer deadline day with a loan move for Aaron Ramsey from Juventus that no-one saw coming, so don't rule out another late blockbuster arrival ahead of the club’s return to the Champions League.
England midfielder Ross Barkely has been linked following his departure from Chelsea, along with Brazilian midfielder Evander from FC Midtjylland, who is valued around the £8.5million mark.