With 18 holes remaining at St Andrews, the leading 25 players are separated by just five strokes, setting up an enthralling closing round over the Old Course on Monday.
Looking ahead to the final round, the South African told Sky Sports News HQ: ???This is an exciting finish today. Jason Day, who has a magnificent swing, has been knocking on the door in a lot of majors.
???It would be nice to see him win. It would also be nice to see amateur Paul Dunne win or Jordan Spieth win ??? there???s a whole host of players it would be nice to see win.
???Today, the man with the right mind will win. Not long hitting, as everyone continually talks about.???
And what advice would Player give Paul Dunne, the amateur who shares the lead after 54 holes.
Player, who turns 80 in November, added: ???It???s an outstanding achievement. It would be really exciting if he could win because the last amateur to win The Open was Bobby Jones in 1930.
???Nobody expects him to win. He???s got nothing to lose. But be aggressive. You???ll not win by playing safe. Rip it at the flags and believe in yourself.???
Another player who could make history on Monday is Spieth. The 21-year-old American is one stroke off the pace and if he could lift the Claret Jug it would make him only the second golfer ever to win the Masters, US Open and Open in the same year.
Player said of Spieth: ???He???s refreshing. He speaks well. Always looks tidily dressed. He comes up with the right answers.???
And Player has stressed it would be good for golf if 14-time major winner Tiger Woods could rediscover his old form.
The American has not won one of the big four events for more than seven years and Player offered this advice: ???Tiger needs to re-start from the beginning ??? mentally, physically and theoretically.
???He doesn???t swing the club correctly. He???s confused. He???s had lessons from all these different pros and they have all given him something different to think about.
???He won the US Open by 15 shots (back in 2000) and the next week he???s having a lesson and I don???t understand it.
???If he had never had another lesson after winning the US Open, I guarantee you he???d have broken all records, would have gone done in history as the greatest player of all time. He???d have won at least 20-22-24 majors.
???It???s actually very sad. But it can come right. But he has to find someone who has been in the arena and understands the game, knows how to think ??? because it???s not just about the swing.
???It can come right and I hope it does because we need him in the game.
???Golf has always been a white sport and I know when he came to South Africa all these wonderful young black kids came out to see their great hero.
???He inspired millions of people. We need him back for the good of the game.???