Both Old Firm rivals do battle at Parkhead on Saturday and the Celtic skipper is wary of the ever-improving Gers since the 43-year-old has taken charge.
Rangers' failure to hire a long-term replacment for Pedro Caixinha saw Murty given the role until the end of the season, and the former Reading defender has done a decent job.
The Ibrox side bounced back from two successive defeats by beating Motherwell 2-0 on Wednesday night to make it seven victories in 11 Premiership games for Murty.
In that time, the Ibrox side managed to win four Premiership matches in a row, the first time that Rangers have won three or more on the spin for a year, and the Celtic star has conceded that his bitter rivals have come on since he took over from the Portuguese in October.
He said to Sky Sports News: "I think they [Rangers] have improved under Graeme. I think he has done a good job with them. It was obviously hard job coming in to be caretaker.
"It is a huge game for us. It is at Celtic Park so we have got to make sure that we dominate the game.
"We are all looking forward to it, plus it gives the fans the bragging rights for the next couple of weeks going into the winter break."
If Rangers have designs on winning the Premiership, victory is a must. Brendan Rodgers's side are 11 points clear of the Gers for now and, realistically, that needs to be eight by full-time on Saturday otherwise it's most likely going to be seven titles in a row come May.
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