The actor cemented his status as a movie star with his role in the 1989 picture, which takes place on a cornfield in Iowa that has since become a popular tourist destination.
It is believed owners Don and Becky Lansing wanted Costner to own the land and made him a private offer, but the star turned it down and they placed the field on the market for $5.4 million (£3.6 million) last week (ends16May10).
Former Major League pitcher Ken Sanders, who is overseeing the sale, tells TMZ.com Costner was offered the chance to buy the land last year (09) and snubbed a second offer earlier this month (May10).
Costner's Field of Dreams co-star Ray Liotta has denied rumours he's looking to buy the property - but hopes the new owner will maintain the baseball field.
He tells E! Online, "I could understand if they don't because you gotta (sic) make a living. But you probably would make more now charging people to see the field than planting corn. I've heard from people who have taken their son there or they make a pilgrimage once a year.
"There are fantasy baseball things that happen there, too. I think it's more than just about the field like the movie was - it wasn't really just about baseball."