The Reds have been monitoring the availability of both players for some time, with a failed bid for Adam in the January transfer window.
Liverpool are thought to have agreed a £10million fee for the Tangerines captain who caught the eye of the Premier League last season. Part of his fee goes to his former club, Rangers, and reports suggest a season-long loan of Jonjo Shelvey to Bloomfield Road is part of the deal.
England international winger Downing recently turned down a new contract at Villa and is thought to be on the verge of a £15million move to Merseyside.
Reports over the weekend suggested the Reds have also put in a late £22million offer for Blackburn Rovers centre-back Phil Jones in a bid to scupper Manchester Utd’s interest in the England Under-21 international.
Ipswich Town’s Connor Wickham also remains a prime target of Kenny Dalglish’s, with a fee of around £9million being speculated.