The Reds had been hopeful of tying up a deal for the England international before his departure for World Cup preparations, but a fee is yet to be agreed with the Saints.
Lallana has now flown out with Roy Hodgson’s squad for two pre-tournament friendly games in the USA this week.
The BBC’s Ben Smith reports:
The midfielder has not put in a transfer request but has made his feelings known to Southampton.
Liverpool have made a £25m offer for the Saints captain.
Liverpool completed the signing of Lallana’s Southampton teammate Rickie Lambert on Monday — the 32-year-old saying it is a “dream come true” to move to Anfield.
Southampton Football Club can confirm that we have received multiple offers for some of our players in the past weeks. This is a confirmation of the depth of the development that is ongoing in our academy and of the present standing of our first team within the Premier League.
We are staying true to our plan and vision and, as a result, we have no need to accept any offers. We are deep in the process of appointing a new manager who will continue to move our club forward. It remains our preference not to partake in any transfers until the new manager is in place. Our scouting & recruitment department continues to monitor targets we have identified to improve our squad, and the new manager will have final input into our recruitment process.
BBC Radio Solent’s Adam Blackmore says Southampton aren’t satisfied with Liverpool’s offer:
— Adam Blackmore (@bigadamsport) June 2, 2014
The saga continues.