BBC Radio Solent claims the Reds have already made a bid for the midfielder's services, with Lallana having enhanced his reputation enormously this season, starring both for the Saints and England's national team.
Last week, ESPN revealed the Reds were interested in cutting a deal to sign Mauricio Pochettino's star playmaker, mooting that a £20 million offer had already been made.
Those claims are gathering pace ahead of this summer's 2014 World Cup, which Lallana will be hoping to feature in as part of Roy Hodgson's Three Lions squad.
Per the ESPN report, Rodgers commented on his speculated interest in Lallana, speaking highly of the player's talent. In response, The Times' Oliver Kay deduces that Liverpool are indeed closing in on a deal:
The 26-year-old's seat on the plane to Brazil may well be deserved, too, as Squawka shows that no other English player created more chances than Lallana this season:
In helping the Saints to an eighth-place finish in the Premier League this term, Lallana has succeeded not only in boosting his own prospects but those of the south coast club, too.
And chairman Ralph Krueger is fully aware of the transfer interest such improvements are bound to attract, but, when speaking to BBC Radio Solent on Sunday, remained stoic in his fight to hang on to Southampton's strongest individuals:
The reason people look at our players is because the club does an excellent job developing them. 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.
It's a double blow for the Saints as the Mirror's David McDonnell also reveals that Manchester United are on the brink of luring Luke Shaw to Old Trafford in a £25 million coup, which could be the first of several high-profile departures at St. Mary's this summer.
As the BBC's Phil McNulty points out, it's a harsh reality that Southampton receive little allowance in time to celebrate their achievements:
Southampton have had a terrific season considering it's only three years since the club were playing in League One, two divisions away from their current lofty standards.
However, even with that rise to prominence, the club won't be able to compete with some of the amenities that United and Liverpool can offer, with Lallana possibly set to number among the club's summer casualties.