According to the Metro, a £20 million offer has been lodged with Southampton for Lallana, who has enjoyed a superb season at St Mary’s.
Liverpool are keen to get this transfer done before the 2014 Soccer World Cup begins, so are expecting a quick answer on their bid.
Ashley Cole, who will soon be a free agent, has also been offered a one year contract at the club.
Chelsea's Cole man could be a temporary solution to Liverpool's left back problems, but both Real Madrid and Monaco are also interested in the England defender.
Liverpool hope to get the green light for both players early next week.