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.”
Negotiations are understood to be ongoing over advancing Scotland international Souttar’s move to Rangers after the 25-year-old signed a pre-contract agreement with the Ibrox club earlier this month.
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, 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.
“I don’t think relaxed is the right phrase for (the situation with out of contract players),” he said.
“I am a coach who will always be alert. I always had as a player that the most important thing is that you feel comfortable and happy in the place that you are. Obviously that is very important to achieve success.
“With contracts ending in the summer with players, I know if the feeling is there for them to continue and to keep their focus on Rangers.
“But you also know that when players are out of contract, maybe they feel they need another challenge or maybe want to move. Either you sign a new contract and you continue with the relations you have or you take a different pathway.
“In the end, it is all good. When you have players going out, you need to get players in. It is a continuous process and not new to me as a coach. You have to make sure you are making the right decisions if there are decisions to be made.”