The 24-year-old midfielder is set to enter the final year of his contract at Leipzig this summer and is believed to be keen to move on as he seeks a new challenge.
He has suitors in the Premier League, where Jurgen Klopp’s Liverpool and Antonio Conte’s Tottenham are suggested to be interested in snapping him up.
Bayern Munich coach Julian Nagelsmann is a big fan of Laimer as well and has asked the club to try and sign him in the next transfer window.
But according to German Bild, the German champions are not ready to offer the kind of money that Leipzig want for him this summer.
The Bundesliga outfit want more than €20m before agreeing to sell the midfielder in the coming months.
Given his contractual situation, Bayern Munich are not prepared to fork out such a sum for a player who could be available on a free transfer next year.
With interest from the Premier League, Leipzig believe they will get the money they want for the player in the summer.
Nagelsmann is hopeful that a compromise can be reached between the two clubs for him to sign Laimer ahead of next season.