Goal reported last month that the Reds, Chelsea, Manchester United and Tottenham were monitoring Lallana with a view to a possible summer move.
Recent days have seen renewed speculation linking the 25-year-old with a move to Anfield and Rodgers admits he is a big fan of the Southampton star.
"Adam is a terrific young talent and player but for us there's always speculation about top young players," the northern Irishman told reporters.
"I saw something on [the reports] yesterday and I'm sure you can respect that I would never mention another player at another club. It's purely speculation."
On Thursday Lallana hinted that he wants to stay at Southampton beyond the summer after accepting the club's Player of the Year award.
"The club means the world to me," he said.
"I've been here since I was 12 and I want to keep progressing with the club. I just hope we can make strides forward in the summer and just keep going from step-to-step and doing well.
"I've got a great relationship with the fans. We've been on a journey, and this is the icing on the cake."