Rangers appointed Beale as the successor to Giovanni van Bronckhorst last season to make the Gers competitive again.
This season, the Rangers hierarchy have backed Beale in the transfer market and he has brought several new faces to Ibrox.
Despite strong backing, the Rangers are out of the Champions League after a defeat against PSV Eindhoven in their qualifying round tie and they are fourth in the league table.
Rangers’ defeat at the hands of arch rival Celtic at the weekend has raised doubt over Beale’s future at Ibrox.
And it has been claimed that Birmingham City boss Eustace is high on Rangers list to replace Beale if they do make a change.
It is said that Eustace’s work last season with Birmingham City caught the eye of the Rangers hierarchy.
Birmingham City are sitting in fourth place in the Championship table this season and it remains to be seen whether an offer from Rangers will come to Eustace in the coming weeks or months.
