The pair will reunite when Everton host Palace in the Premier League on Saturday, following Allardyce's exit from Selhurst Park at the end of last season.
Serbian international Milivojevic has said that, while he was shocked to learn of the manager's departure, the two will "shake hands" after Saturday's game.
"We heard on the morning he left that he wanted to retire from football and we were not happy because we had good results under him," the 26-year-old told reporters. "We did not expect that. It was a shock for us. But that is life.
"We stayed in the league together and for sure he was one of the best managers I have worked with. We are going to give our all to beat them but before and after the game we are going to shake hands because we had great memories."
Milivojevic netted an equalising penalty in Palace's 1-1 draw with Newcastle United last time out.