Former footballer Murphy, 37, was appointed when Mark Hughes was manager.
However there has been talk of a rift with current boss Roberto Mancini, stretching back to earlier in the campaign, over City's injury list and that he was being downgraded.
But the club claimed in a statement that at no time was Murphy demoted nor did he work at any time or in any capacity in the Academy.
The statement added: "We would like to thank Jamie for all his hard work and endeavour during his time at the football club and wish him every success in his future career."
Source: PA
Source: PA