Cooper gave the cap to his friend John Semple after playing in Scotland's 3-1 loss to Egypt in 1990 and auctioneers believe it could now be worth up to £8,000.
The winger, who played 22 times for Scotland during his career with Clydebank, Rangers and Motherwell, died in 1995 of a brain haemorrhage at the age of 39.
He was a popular figure in Scottish football and Mr Semple hopes the sale will be of interest to fans.
"I got to know Davie through his brother John and over the years we forged a strong friendship," he said.
"I have had the cap for a number of years and now that I'm getting older I thought the time was right to pass on this important piece of sporting memorabilia to another football fan who appreciates Davie's immense talent as much as I do."
It has been described as an "incredibly important" piece of memorabilia and will be sold at McTear's Auctioneers on June 17.
McTear's managing director Brian Clements said: "There is no doubt Davie Cooper is one of greatest players ever to come out of Scotland.
"His talent was immense and he was admired by fans and players alike.
"Cooper's last Scotland cap is an incredibly important piece of sporting memorabilia and I have no doubt it will generate a huge amount of interest when it comes up for sale."
Before the auction, the cap will be on display in McTear's and at a stand at the Ideal Home Show Scotland at the SECC in Glasgow this weekend.