The Anfield right-back is currently recovering from an ankle complaint, and he missed Liverpool's most recent game, a 1-0 home defeat to Southampton.
Liverpool typically offer first-team players with less than two years left on their current contracts a new deal to warn off interest from rivals - but Glen Johnson will be 31-years-old when his expires.
And the Reds are less eager to commit long-term to players over the age of 30 - even if they're established starters.
The report claims Liverpool's owners, the Boston-based Fenway Sports Group, are still keen to discuss terms with the England international, but he'll have to wait until the end of the campaign.
It cites the experience of Steven Gerrard - the Reds captain only signed a new contract once his current deal had just 12 months left to run.
And it goes on to warn the two parties - Liverpool and Johnson - could reach a stalemate over salary demands.
Johnson is one of the club's highest earners, but Liverpool will be reluctant to offer a player over the age of 30 a salary increase.
It remains to be seen whether the former-West Ham full-back is willing to accept a deal which offers his existing - or even a reduced - weekly wage.
He remains one of Liverpool's most important players though, and would be sure to attract plenty of interest from top-six clubs should his contract run down without an agreement reached.