Klopp is believed to earn around £7million a year and Fenway Sports Group have made an approach to raise his salary to £10m following Liverpool’s Champions League triumph.
Club owners are keen to reward Klopp with another six-year deal extension worth £60m, which would also ward off any raid from their European rivals.
The German manager is believed proceeding with caution, however, when it comes to putting pen to paper on another new deal.
According to reports, Klopp values his health far more than money and does not want to put himself under undue stress by committing to another lengthy contract.
In the summer of 2016, Klopp and his coaching staff signed six-year extensions to their deals keeping them at Liverpool until 2022 and there is no suggestion he is considering quitting before that expires.
By the end of the 2021-22 season, when his current deal expires, he will have been at the helm for seven years and FSG are fearful that the more successful Klopp becomes the more attractive he makes himself to interested parties.
Yet his reputation as an elite manager has soared since he re-built Liverpool, not only taking the club to a sixth Champions League success but also to last season’s 97-point second-placed finish.
Klopp remains intent to end Liverpool’s 29-year wait to be kings of England again.
But he is taking longer than expected to consider his long-term options.