It emerged 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 player....there is always speculation," he told reporters.
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."