The Gers have compiled a three-man shortlist to find a successor to Gerrard, who left the club to become the manager at Premier League club Aston Villa.
Van Bronckhorst has emerged as the frontrunner to become the next Rangers boss and the club are keen to sort out the appointment soon.
According to Dutch daily De Telegraaf, a delegation have been released by the club to meet the Dutchman to convince him to return to Glasgow.
The 46-year-old has been out of work since leaving Chinese Super League Guangzhou in December last year and is keen to return to management.
He is keen on the Rangers job but wants to hear the project on offer before committing to anything.
Rangers are hoping to convince their former player to pack his bags and arrive in Scotland in the coming days to take charge of the team.
The club are keen to sort out the appointment soon and are hopeful of working out a deal with the Dutchman shortly.
Rangers want a new manager in place before they take on Hibernian in the Scottish League Cup semi-final next weekend.
