The United States international is due to have a medical on Sunday with a view to completing the temporary switch before the transfer window closes on Monday.
Bradley is the son of United States head coach Bob Bradley and was part of their World Cup squad in South Africa last summer.
Villa boss Gerard Houllier would only say: "I don't want to say anything about it, maybe in two days' time."
But Villa sources are optimistic 23-year-old Bradley will become Houllier's fourth signing of the current window after Darren Bent, Jean Makoun and on-loan defender Kyle Walker.
Bradley played for the MetroStars and New Jersey in the MLS and then had a spell with Heerenveen before moving to Borussia two-and-a-half years ago.