Minogue, 50, had been due to appear at the final night of the event in 2005 but had to cancel her performance in order to undergo treatment for breast cancer.
UK dance music duo Basement Jaxx were eventually drafted in to replace the Australian singer.
Minogue later made her debut on the Pyramid stage with a guest appearance during US group Scissor Sisters’ set in 2010.
When asked by the Press Association if she would like to be offered another chance to close the night at next year’s festival, Minogue said: “When I was supposed to do it I think I would have been the first solo female to headline in however many years it was, so I was really proud of that at that time.
“Obviously it didn’t happen. So yes, it would be amazing and very emotional to be standing there and doing what I didn’t get to do all those years ago, for sure.”
Minogue was speaking ahead of her arena tour of the UK and Ireland in support of her number one album Golden, the 14th LP of her recording career.
Before heading out on the road the former Neighbours star will be playing an outdoor show for BBC Radio 2 in Hyde Park on Sunday September 9.
Minogue said that over 10 years on from her Glastonbury heartache she was now able to put on an even better show there than the one she planned to do in 2005.
She said: “I think I’m better equipped to do it now actually. Since that time I’ve done quite a few festival gigs and outdoor shows and I absolutely love being out there.
“It’s something different. With an arena tour you are creating your own world. But with the show in Hyde Park, you don’t know if it’s going to rain, or thunder or be baking hot - there’s this other dimension to it.
“You can’t control the environment and especially, historically at Glastonbury. So the short answer is yes, of course it would be incredible to play there!”
Kylie Minogue will tour the UK and Ireland in September and October, with the first show to take place at Newcastle Metro Radio Arena on Tuesday September 18.