The BBC pundits found themselves at loggerheads during a joint interview with the Independent.
The former Arsenal hard man insists the young Everton centre-back is not ready for the demands of regular international football, adding that boss Roy Hodgson should instead focus on improving Chris Smalling and Gary Cahill.
He said: "It's too early for John Stones. He is one for the future. But we need to protect Smalling and Cahill better. The Leicester defenders [Robert Huth and Wes Morgan] get a great deal of protection, we need to do something similar for England. Eric Dier can do that and Dele Alli will do that as well.
"The ball is always going to come into the box. You can't be sure that we can stop every cross. So you have to be set up correctly in the box. Don’t be surprised the ball is coming in. If the striker can read it so can I. It’s not enough to say that players have formulated their bad habits: you come together as a team, work and iron it out."
Stones was named in Hodgson's line-up for last weekend's friendly with Turkey at the Etihad, where he largely struggled to keep tabs on the lively Cenk Tosun, but he is still expected to be named in England's final 23-man squad.
The 21-year-old was reportedly the subject of three bids from Chelsea last summer, who were then under under the stewardship of Jose Mourinho, and the Portuguese manager's imminent return to English football with Manchester United has again seen him linked with a move away from Goodison Park.
Former Liverpool star Murphy agrees that Stones is destined to reach the very top, adding that he should already be ahead of his defensive teammates in the England pecking order.
He told The Independent: "100 per cent I think Stones should play. If you're going to not play him you are going to have to have two centre halves who are really solid and don’t make mistakes, otherwise why are you sacrificing him? He does make the odd mistake by trying to play out but he's our best footballing centre-half by a mile. I like Cahill and Smalling – they are both solid. Cahill has played in a Championship winning side – but they both make mistakes as well."