'Fear the Brow' Owner -- Anthony Davis Can Have My Trademark ... For a Price

Anthony Davis will have to pay through his nose if he wants to buy the famous "Fear the Brow" trademark -- at least according to its current owner, who tells TMZ, he doesn't plan to sell out for cheap.

Reid Coffman -- owner of the University of Kentucky apparel store Blue Zone -- trademarked "Fear the Brow" last November for his popular Davis-themed merchandise. Davis attempted to trademark the SAME phrase earlier this month.

Davis -- who was drafted to the New Orleans Hornets last night -- hasn't officially challenged Coffman's trademark, but his recent trademark filing is a clear sign Davis plans to go to war over the slogan.

Unfortunately for Coffman, it's not a cut-and-dry case just because he filed first. Anthony arguably has a viable claim to the trademark because the "Fear the Brow" slogan trades off his persona, particularly his extremely unique face hair.

Nevertheless, Coffman insists he owns the full rights to the trademark because he created the slogan -- and if Davis wants to buy it ... he's willing to play ball.

Coffman wouldn't specify a selling price -- but tells us, "If someone like Nike took this slogan over it could be worth millions." Coffman says he's currently ready to accept offers.

Calls to Davis' reps were not returned -- but moments before he was drafted, Davis was asked about the trademark filing ... and he responded, "My agents and my parents talked it over and they came at me with the idea. And I loved it. Who doesn't love money?"