Snell was not sure what Te Papa had done to establish the veracity of the singlet, compared to other clothing.
The singlet with the number 466 on it was thought to be the one worn by Snell when he won two of his gold medals, in the 800m and 1500m at the Tokyo Olympics of 1964. His first had come in the 800m at the Rome Olympics of 1960.
Snell admitted that most of his Olympic apparel was now gone, either donated to charity or given up at auction.
He was left with nothing from his Olympic or Commonwealth Games appearances.
He had been considering donating his medals to the museum, to go with the singlet, but said that he would now be re-thinking that idea.
"The amount of money that the museum was prepared to pay, that was very surprising," Snell said.
"It was so surprising that I felt if they were prepared to do that then I should perhaps give them my medals to go with it.
"I'm going to have to rethink seen as there is no singlet anymore."