The Rangers caretaker has claimed there's been movement in the Ibrox side's manager search, and former Celtic striker Sutton could not resist a dig.
Murty took charge of Rangers more than a month ago after Pedro Caixinha's sacking, but the Glasgow giants are not yet close to making an appointment, according to the former Scotland right-back.
"There has been movement but we're not quite there yet, and I think that to get the next five, six, seven years right, we need to take our time now to get this appointment right," said Murty, as quoted by Sky Sports.
And Sutton, who spent six years at Celtic Park, could not resist a dig in Rangers' direction after the 43-year-old's comments.
Movement!! Not like it’s taken very long... https://t.co/RincdTkavw— Chris Sutton (@chris_sutton73) November 28, 2017
That prompted Celtic fans to get involved too, some of whom are suspicious about the timing of Murty's comments, ahead of Rangers' AGM on Thursday.
Bowel movement— Joe Hamilton (@JoeRangzen) 28 November 2017
just in time for the AGM - appease the berzzzz— Steve Boyd (@Steve_AR1) 28 November 2017
They have to say that before the AGM on Thursday.— Nikki. (@nicnakpaddywak1) 28 November 2017
He means they've moved from the 19th century to the early 20th.— Scott-E (@ScotticusE) 28 November 2017
Obviously someones donated a packet of senokot.............— Gerry Keegan (@gerrykeegan56) 28 November 2017
Speaking to Talksport on Tuesday morning, ex-Rangers midfielder Ray Wilkins pleaded with the Ibrox powers-that-be to enlist the help of several club legends - including himself - in their quest to restore the club to its former glories.
Rangers have won two and lost two with Graeme Murty in temporary charge, and sit fourth in the Scottish Premiership standings - nine points behind Celtic having played a game more.