"We are nearly there on the personal terms and he is doing a medical at the moment. Hopefully, we'll have good news for Liverpool fans probably tomorrow morning."
Media reports estimate the fee will be worth 25 million pounds.
If the deal goes through Lallana will rejoin former Southampton team mate Rickie Lambert who was also a member of the World Cup squad and moved to Liverpool this month.
Lallana, 26, made 235 league appearances for Southampton, scoring 48 goals.
His form for the south-coast club earned an international call-up but he was involved in a disappointing World Cup campaign as England failed to progress beyond the group stages in Brazil.
Earlier on Friday, England defender Luke Shaw left Southampton for Manchester United for a reported 30 million pounds.
Liverpool, who finished runners-up to Manchester City last season, also signed midfielder Emre Can from Bayer Leverkusen this month.
(Writing by Tony Jimenez, editing by Ed Osmond)
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