Signed from Olympiakos in January 2017, Milivojevic has been crucial in helping Palace avoid relegation for the past two seasons.
The 27-year-old was named club captain shortly after arriving at Selhurst Park and has become a fan favourite due to his ferocious style of play.
It has been a meteoric rise for Milivojevic, who has continued to improve at every level. After breaking through the first-team ranks at Serbian Premier League club FK Rad, Milivojevic earned a move to Red Star Belgrade and then Anderlecht before arriving in Greece.
Milivojevic has also excelled at international level, having won 30 caps for Serbia since making his debut against Chile in 2012.
Milosavljevic, who scouted players for Arsenal for 15 years, knows Milivojevic well having trained him personally in Serbia. And he thinks there could be bigger things on the horizon for the 6ft 1in midfielder.
Asked if Milivojevic could move to a bigger club in the future, Milosavljevic told Tribalfootball: "I think yes. I know Luka very well.
"I (conduct) personal training and I once trained with Luka for three or four months for every day.
"He has many qualities. But I explained to Luka to look at Steven Gerrard. He can do the same but he needs somebody to push him because he must make many sprints at 100 per cent.
"This is a problem in Serbian football. If you watch Serbia at the World Cup, not many players make sprints with repetition."