Southport are currently 16th in the Vanarama National League North with Davies taking over from Alan Lewer, who left by mutual consent at the end of September.
The Sandgrounders have lost their last five league games, conceding 18 goals in the process.
The 40-year-old played under Allardyce at Bolton and the former England striker turned to him ahead of getting the job.
"Sam's had a massive influence on my career," he told ITV. "I had a long conversation with him prior to taking this job and when I got the job he was one of the first people to ring me.
"We had a good chat yesterday about things he would look to do in this situation, obviously I will have my own way of doing it.
"It's important for me not to change and be myself as a person. People say you need to be hard but I'm going to be myself and it has worked for me throughout my career.
"I think the clubs I have played for, other than Blackburn Rovers, have all had success and created a bit of history with cup finals and getting into Europe. That's what football's about and I'm looking forward to create some nice memories here."
Davies first game in charge tomorrow is at home to second from bottom Gainsborough Trinity.
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