The Austria international was interesting the Reds and Bayern Munich over the summer.
In a recent interview with BILD, Laimer, sparked fresh speculation that he could be on his way to Anfield in the near future after admitting he is a fan of the club.
“I'm generally a football fan. I generally like watching the Premier League. I've always been a Liverpool fan," said Laimer. “Surely there are such thoughts. I don't think a club (Bayern Munich) like that comes knocking every summer, it's one of the best in the world.
“I'm a here and now focused. If you worry too much, you lose sight of the most important thing – and that is playing football and getting better. I've been at Leipzig for five years and I feel good. Now it will be a year longer and then we will see what happens.
“When you're associated with clubs like this, there's a certain pride. But I'm more the guy who talks to people and needs a feeling that everything fits together."