The veteran duo are reported to have had a furious row with Murty following Sunday's 4-0 Scottish Cup semi-final defeat by Celtic at Hampden.
Apparently they were involved in an angry exchange with the Rangers manager and are now to be called to a meeting with the club today to find out their punishment.
Brendan Rodgers' side outclassed their bitter rivals with Callum McGregor, Tom Rogic, Moussa Dembele and Olivier Ntcham on the score-sheet.
Former Scotland striker Miller, 38 was an unused substitute at the weekend. Should they be suspended if they spoke out against Murty?
The move could effectively end Miller's career with Rangers as his contract is set to expire at the end of the season.