The Reds have previously had £12.5million and £15million bids for the winger rejected by Villa.
Arsenal were also keen on the winger, but Downing is keen on a move to Liverpool.
The 26-year-old is now set to undergo a medical and discuss personal terms with the Reds.
A statement released on the Reds’ official website read: “Liverpool FC tonight announced they had agreed a fee with Aston Villa for the transfer of Stewart Downing.
“Liverpool have now been granted permission to discuss personal terms with the player and arrange a medical.”
