On Sunday afternoon, Rangers succumbed to a 4-0 defeat at the hands of Celtic in the Scottish Cup semi-finals, with the match seeing Andy Halliday react angrily to being substituted just before half time.
However, according to The Sun, tensions boiled over further in the dressing room with captain Wallace - who was not involved in last weekend's match - openly criticising Murty.
The report claims that Miller then became involved in what has been described as a "major" disagreement, and the hierarchy of the Glasgow giants appear ready to take action by backing their manager.
Wallace faces the prospect of being suspended while veteran forward Miller - who is 38 and out of contract in the summer - is likely to be sacked on Tuesday.
Miller has made 299 appearances for Rangers in all competitions across three periods at the club.