Midfielder Lallana, 26, has been a key player for Saints this season, scoring 10 goals in 42 appearances and earning three England caps.
He is set to be named in England’s World Cup squad on Monday and admitted in Sunday’s pre-match programme he has aspirations to play at a higher level.
“I’m ambitious,” he said. “I want to one day play in the Champions League.”
Speaking on Sunday, Southampton chairman Ralph Krueger said he expected interest in the club’s star players.
“The reason people look at our players is because the club does an excellent job developing them,” Krueger told BBC Radio Solent. “It should be difficult here every summer.
“It is really important that people respect that there will be conversations going on, beginning on Monday, with clubs. That is part of the business.”
Saints team-mate Luke Shaw is also being linked with a move away from St Mary’s with Manchester United reported to have bid £27m for the left-back.
Lallana came through the Southampton academy, which also produced Gareth Bale, Theo Walcott and Alex Oxlade-Chamberlain, and has become an integral member of a side that achieved its highest Premier League points total this season.
Saints finished eighth with 56 points and Lallana’s form earned him a place in the Professional Footballers’ Association Premier League team of the year, along with Shaw.
He made his England debut against Chile in November and has since played against Germany and Denmark.
Lallana, who was spotted by Southampton playing for Bournemouth’s centre of excellence, is wanted by a Liverpool side who narrowly missed out on their first Premier League title in 24 years.
Brendan Rodgers’ team finished two points behind eventual champions Manchester City, who won their second title in three years on Sunday.