Former Middlesbrough player Downing has been a key summer target of Liverpool boss Kenny Dalglish, and talks with the 26-year-old can begin.
Liverpool said in a statement on their official website: “Liverpool have now been granted permission to discuss personal terms with the player and arrange a medical.”
Villa had rejected bids of £12m and £15m from Liverpool, and manager Alex McLeish insisted he wanted Downing to stay in the midlands.
Downing made it clear only last month, when on England duty, that he would not sign an extension with Villa
Should the deal for Downing be concluded, he would become the third high-profile midfield recruit by Dalglish this summer, following the signings of Jordan Henderson from Sunderland and Charlie Adam from Blackpool.