The 53-year-old told Tynecastle directors they had to alter their management team, which is overseen by director of football Craig Levein, and gave them a plan of his ideas. However, they were rejected and he has now withdrawn from the race to succeed the sacked Ian Cathro.
Davies dropping out follows news that previous candidates Dougie Freedman and Steve McClaren have taken jobs at Crystal Palace and Maccabi Tel Aviv respectively. Steven Pressley, Paul Hartley and interim head coach Jon Daly remain in contention for the position.
In a statement released by Superior Sports Management, which represents the former Derby County and Nottingham Forest manager, Davies said: “I spoke to Hearts, looked at their structure and gave them a clear plan on how to alter it to improve the club.
“It appears they are not ready to make the internal changes required to achieve greater success. It seems to me they just want to change the figurehead. It’s my belief just changing the manager will not achieve what’s required for success and perhaps the alterations are outwith their financial boundaries at present.
“I wish them well in their future endeavours.”