The Republic of Ireland player has reportedly made it known to Hoops' manager Neil Lennon that he wants to leave the club he has been at since a schoolboy.
Russian side Spartak Moscow have already had a reported bid of £8.3million turned down while the 24-year-old, who has long harboured ambitions of playing in the Premier League, has been linked with Birmingham and Aston Villa.
Auld, who won the European Cup with Celtic in 1967 when they beat Inter Milan 2-1 in Portugal, said that Lennon must use any money from McGeady's sale to make necessary improvements to the squad, which ended last season empty-handed.
"When Aiden leaves Celtic he can hold his head up high," Auld said.
"Every club and every stadium in Scotland has seen him play well.
"He's not just skilful, he has heart and is brave.
"I watch him getting abused on the park but he just picks himself up and dusts himself down.
"He never hides and is always looking for the ball.
"But he's not the finished article. He has a lot to learn, especially with his final pass, and I have always said that if a player wants to go then don't stand in his way.
"Every club is a selling club. Celtic and Rangers have been selling players away back to when I started playing in the 1950s.
"It will be very difficult to replace him but one player doesn't make a team."
"But if we can become a better team with one player going then we must do that," Auld continued.
"The squad needs surgery. We don't need players - we need good players.
"I'm not sure who Celtic are looking at but whoever we bring in must be quality.
"We need three or four good players who will lift the crowd and lift the dressing room.
"It was so disappointing last season for all the supporters and it has to pick up this year.
"At the moment the fans' heads are down.
"I hear all the time that they won't be selling their season tickets.
"I think they will but they need some entertainers."
Auld, who left Celtic for Birmingham in 1961 but returned to Celtic Park four years later, believes Russia might not be the most suitable destination for McGeady.
He said: "I don't think he will go to Moscow, that might be too far away for him.
"It's okay when you are playing football, that is the same wherever you are, but returning to your digs or house every night when you don't have your family or friends around is difficult.
"I see him going down south and playing his football down there."