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?"

NBA DRAFT: Number-One Pick Anthony Davis Goes to New Orleans

Anthony Davis was the number-one pick by the New Orleans Hornets in today's (Thursday's) NBA draft.

Kentucky's Anthony Davis was the number-one pick by the New Orleans Hornets in today's (Thursday's) NBA draft. And one of Davis's former teammates was close behind. The Charlotte Bobcats picked fellow Kentucky alum Michael Kidd-Gilchrist as the second pick, making it the first time that the first and second picks in the draft came from one school.

In other NBA news, it appears that Lamar Odom is headed back to Los Angeles for a second run with the Clippers as part of a three-team deal.