The 24-year-old midfielder will have a year left on his contract at RB Leipzig in the summer and the German club want to offer him a new deal to keep hold of him.
The Bundesliga outfit want to secure his future, but the player is undecided about whether to sign fresh terms with them.
According to Sky Sports Deutschland, the midfielder can imagine playing his football in the Premier League, something which will boost Jurgen Klopp’s hopes of signing him, if he pushes to take him to Anfield.
Liverpool have been credited with an interest in Laimer, but at least one more club from the Premier League top five have their eyes on him as well.
It has been claimed that several other Premier League sides have their eyes on Laimer ahead of the summer.
His name is being mentioned in several recruitment meetings across teams in the top flight of English football.
Manchester United have also looked at him but the trail leading to Old Trafford is cold compared to others.
Leipzig are likely to want to sell him in the summer if Laimer does not sign a new contract with the club.