But van Bronckhorst indicated that he remains comfortable with the situation should Rangers be unwilling to meet Hearts’ asking price for a permanent deal to go through before next Monday.
“I said before, we are happy that John will join us next season,” he said. “I think he will only come this window if we think it’s the right thing to do. If not, we will welcome him in a couple of months.”
Van Bronckhorst confirmed that the Scottish champions are looking to add at least one more player to their squad before next Monday night’s deadline.
Romanian playmaker Hagi has been ruled out for the rest of the campaign after undergoing surgery on the knee injury he sustained in last Friday’s Scottish Cup fourth round win over Stirling Albion at Ibrox.
“Of course it is a big blow and we miss an important player who is not available for the coming months,” said van Bronckhorst.
“We are looking to add a player to the squad but it needs to be a player who we think is right. You don’t want to just add a player to make up the numbers, you want to have the balance in the team also good. Otherwise, you are better keeping your squad as it is.
“We are definitely looking to add a player in the coming days. We have to wait. It’s always a crazy time, the transfer window, because you never know what’s going to happen. We’ll just wait and see how it will evolve.”
Van Bronckhorst, meanwhile, is closely assessing the position of eight members of his squad whose contracts expire at the end of the season – goalkeepers Allan McGregor, Jon McLaughlin and Andy Firth, defenders Connor Goldson and Leon Balogun, midfielders Steven Davis and Scott Arfield and winger Brandon Barker.