The Reds have reportedly tabled a £20 million offer for the 26-year-old, although it is thought that the Saints are holding out for an extra £5 million for their skipper.
Lallana's fine form last season has been rewarded with a spot in England's 23-man World Cup squad, and the Three Lions man issued a veiled 'come and get me' plea to the after talking up his hopes of turning out in Europe's premier competition.
Speaking at an event with England sponsors Vauxhall, Lallana said: “I’m ambitious. I have aspirations to play in the Champions League.
“Ever since I’ve played international football, you realise there’s that other level to play at. It would be great. I feel I’ve come a long way, it’s been a special season, not just for me, but for [Southampton] as a whole.