Rangers will unveil new signage on the Govan Stand ahead of their Championship opener against Hearts tomorrow in tribute to their former defender, who died in April, aged 65.
After a legendary playing career that saw him win 14 honours with the Light Blues, Jardine became an important figure off the park and remained influential behind the scenes even during his battle with cancer.
McCoist said: "Sandy would be embarrassed at first, to tell you the truth.
"He would be incredibly proud - absolutely incredibly proud. But he would probably be a wee bit embarrassed at first.
"That's what I think anyway. The bottom line is that it's a wonderful and fitting gesture and we feel it's absolutely the right gesture.
"It's amazing what fate throws up, because we play Hearts on Sunday and he had a close association with both clubs. I just hope that the whole occasion will do Sandy justice."
Jardine becomes only the second man - after legendary former boss Bill Struth - to have a stand at Ibrox named in his honour.
It is fitting that the ceremony should take place ahead of a tie with Hearts.
Jardine supported the Jambos as a boy and played for and managed them alongside Alex MacDonald after leaving Rangers in 1982.
McCoist said: "It will be an incredibly emotional occasion, particularly for Shona and the family. They will be at the stadium.
"But the one thing I can guarantee you Sandy would have wanted would have been for both teams to go at it and put on a good game of football. I'm sure Robbie [Neilson] and our team will do our best to do that."