English defender Goldson has been a key performer for Rangers since his £3 million move from Brighton in the summer of 2018, displaying remarkable reliability and consistency in making 222 appearances since then.
But the 29-year-old’s time in Glasgow appears to be coming to an end as his contract expires next month and he could make his farewell outing for Rangers in the Scottish Cup final against Hearts at Hampden on Saturday.
“Regarding Connor, the club has been in talks with him to extend his contract,” said van Bronckhorst. “So far, he hasn’t extended it.
"The chance he will still be a Rangers player (after) tomorrow will be small but, as I’ve said, I would love to have Connor in the team next year.
"But as you see quite a lot, when players are getting out of contract, there are two possibilities – to keep playing for Rangers or to move on and maybe have another challenge.
“I still have in my mind that he will be part of Rangers next year. That’s my feeling more than the reality. We will have to watch in the coming weeks.
“But I think Connor has been amazing for this team in all of his years as a Rangers player. If it will be his last game on Saturday, I don’t know right now.”
Veteran goalkeeper Allan McGregor, also coming to the end of his contract, may already have made his last appearance for Rangers in Wednesday’s Europa League final defeat against Eintracht Frankfurt in Seville.
Van Bronckhorst has confirmed that McGregor’s deputy Jon McLaughlin will retain his place as Rangers’ Scottish Cup ‘keeper against his former club Hearts at Hampden.
"Jon has done really well in all of the Scottish Cup games that we’ve played – especially in the semi-final against Celtic,” said van Bronckhorst. “For me, it would be strange to change him as we’ve given him the confidence in the cup competition.
"It’s a difficult one because Allan, of course, is our number one goalkeeper but he was very thoughtful and could totally understand. Allan will push Jon and will guide him and support him tomorrow.”