The Lilywhites manager will meet with the Portmore United star and his agent this week to discuss a deal to join the Division One club.
The defender was recommended to Brown by Preston striker Ricardo Fuller, who is a fellow countryman of Davis's.
The 24-year-old is considered one of the best players in Jamaica and has attracted the interest of Birmingham City and Walsall in the past.
Brown will hope talks with Davis prove successful, as he looks to add a central defender to his squad for the new season.
"We meet with Claude Davis and his agent on Tuesday and if things go well with him, then we'll make him the new signing," Brown told the club's official website.
