Manager Neil Lennon's stock is at an all-time high after winning his second Clydesdale Bank Premier League title in succession and guiding his side to the last 16 of the Champions League, with the William Hill Scottish Cup final against Hibernian at Hampden next week to come.
And, while Lennon has been linked with Everton and Stoke, former midfielder Auld - who played in the Celtic side which became the first British team to win the European Cup when they beat Inter Milan 2-1 in Lisbon in 1967 - reckons there is room for improvement.
Auld, referred back to the ethos of his two managers at Celtic Park during his two spells at the club which spanned the 1950s, 60s and 70s, Jimmy McGrory and Jock Stein, as he said: "Neil Lennon is just a young boy and has a lot to learn.
"He has done extremely well. But I am disappointed because we have lost 35 points in the league this year. We had a pool of players that should have run away with the league but didn't.
"We are 13 points clear but the teams who beat us... that was disappointing. I honestly believe that Neil has to bring in three quality players to bring on the young players.
"Whether he is allowed to bring in another couple of players I couldn't tell you, but everybody in the stands will tell you we need another two or three quality players. I also think we need someone who is going to entertain the supporters.
"This is a 60,000 stadium and there are 40,000 season tickets and if you look some games there were only 40,000 there. I think it was because we were winning some of these games but we are not entertaining.
"And that was the last thing Stein and McGrory said to us coming out the dressing room in every game.
"They said 'entertain, you have the ability or you wouldn't be here. These people have paid good money to see you'."