Celtic manager Ronny Deila insists Virgil van Dijk does not want to leave the Scottish Premiership leaders in January.
Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
The left-back underwent surgery in November 2012 and returned in September 2013 for a run of six games - scoring twice against Millwall - before suffering a further setback in October.
Murphy, who turned 30 on Saturday, has been forced to call time on his playing career and told Birmingham's official website: "All of my rehabilitation went as well as it could have done and I managed to return to playing for a brief spell.
"However, I wasn't able to sustain the heights of my previous form and as a result I have no option but to retire.
"Having sought advice from the surgeon and medical staff at the football club, I had to make sure in my own mind that I was ready to retire. I have reached that decision and will look forward to the next chapter in my life."
A club statement added: "Everybody associated with the football club would like to take this opportunity to thank David for his fantastic service to Birmingham City and wish him well for the future."