Van Bronckhorst denied a report that the English defender, who is out of contract at the end of this season, has turned down the offer of a new deal.
But although he insists Rangers sporting director Ross Wilson is still in negotiations with Goldson’s representatives, van Bronckhorst has yet to establish if the 28-year-old is likely to remain a part of his longer term plans for the Ibrox squad.
“I don’t have a clue because I am only here for a couple of weeks,” said van Bronckhorst. “It’s always tough when you have players going out of contract at the end of the season. But, really, I don’t have a clue what will happen.
“Maybe when I talk to Connor myself in the coming days or weeks I will have more of a view on that.
“I spoke to Ross about it today. He is still talking with his agents. So there is nothing new we have to say. It’s still on speaking terms with the agents, so we have to wait.
“I think they are talking. I saw reports he has rejected an offer but that is untrue. They are still talking so hopefully we can have more news in the coming weeks or months.”
Eight other Rangers players are also out of contract at the end of the season - goalkeepers Allan McGregor, Jon McLaughlin and Andy Firth, defender Leon Balogun, midfielders Scott Arfield and Steven Davis, winger Brandon Barker and striker Jermain Defoe.
“It’s the first couple of weeks, so for me the most important thing was to know the squad, know the players and of course win games,” added van Bronckhorst.
“I’ve got to know the squad a lot better than when I arrived. Of course in the coming days and weeks I will also speak with the players about their futures.
“So far, I didn’t because my focus was 100 per cent on winning the games. So far I didn’t have time to speak with the players personally about their futures.”