The white Verde boots are being sold by specialist auctioneer Henry Aldridge & Son later this month and are expected to fetch between £25,000 and £30,000.
If I Can Dream was recorded by Elvis two months after Martin Luther King was assassinated and formed part of his comeback special broadcast on NBC shortly before Christmas that year.
The performance is regarded by fans of The King as one of his “Holy Grails”.
The song was written by Walter Earl Brown and was notable for its direct quotations of the civil rights leader.
Auctioneer Andrew Aldridge said: “Elvis Presley is one of the most iconic figures in music history and we are honoured to be offering for sale the white boots that he wore in one of his memorable performances when he sang If I Can Dream, the song that capped his 1968 NBC TV special.
“Ironically, the very week that the boots are to be sold, Elvis’s album If I Can Dream is set to top the UK album charts - a little over 52 years after the performance he wore these boots for.”