Reports in midweek suggested that the Premier League title contenders were readying a bid for the England international prior to the FIFA World Cup in Brazil.
Lallana looks all but certain to be in Roy Hodgson's travelling party after another impressive season at Southampton in which he has featured in every league game for the club.
But, while Rodgers refused to be drawn on the rumours, he was glowing in his praise of the versatile playmaker.
"I'm sure you can respect that I would never ever mention another player at another club," he said on Friday.
"Adam's a terrific young talent and young player, but there's always speculation about top players."
Rodgers, whose side remain in with a chance of securing the Premier League title on the final day, also reiterated his view that he will agree a new deal at Anfield in the close-season.
Reports suggested a contract solution was imminent but the Northern Irishman stated it would be sorted after the campaign.
"I'm not sure where that (contract) talk came from. I always said it would get done at the end of the season," he explained.
‘Chelsea have to qualify for the Champions League for this season to be a success – they showed that they have the players to perform at a high level, they need a win quickly now’ Blues legend’s fears over recent bad run
'I’d probably pick Cole Palmer alongside Bellingham and Rice in there at the moment. For me, Declan Rice is good enough to play that central midfield role on his own' Thomas Tuchel advised to DROP Manchester City star by England legend
