The football star donned these shirts during the first halves of the group-stage rounds against Saudi Arabia and Mexico, as well as later games against Australia, the Netherlands and Croatia — and the final against France.
Argentina's winning run in Qatar last year was the final feather in the forward's cap, having failed to secure the championship in four previous World Cups.
If the jerseys indeed fetch above $10 million, that could make the sale the most valuable collection of sports memorabilia ever auctioned off, Sotheby's said.
The most expensive individual jersey ever sold at auction was one that basketball legend Michael Jordan wore during his NBA finals run with the Chicago Bulls in 1998.
It sold for $10.1 million last year.
Auction houses have increasingly taken note of sports memorabilia in recent years, considered a growing market.
The shirts are being brought to auction by US tech startup AC Momento, which helps athletes manage memorabilia collections.
A portion of the proceeds will be donated to the UNICAS Project, an initiative with a Barcelona children's hospital that helps kids with rare diseases.
The jerseys will be available for free public viewing when they are up for auction, from November 30 to December 14.