The Romania international has been ruled out for the rest of the season after sustaining a knee injury in last Friday's Scottish Cup win over Stirling Albion.
Hagi, 23, has since had an operation in London, but is set for a lengthy spell on the sidelines, with Van Bronckhorst keen to bolster his squad as a result.
Speaking to the press before Rangers's Scottish Premiership clash with Livingston on Wednesday, the Dutchman said: "It is a serious injury so it is bad news. It is a big blow. An important player is not available for the coming months so we are looking to add a player to the squad.
"But he needs to be a player we think is right. You don't want players in to make up the numbers. You want to have the balance in the team also good. But we are definitely looking to add a player in the coming days.
"I spoke to Ianis this morning, he is in a good place, of course not happy that he has the injury and needed the operation but he's positive and focused on his recovery.