The 19-year-old broke on to the scene with West Ham last season and he has been a key part of Manuel Pellegrini's plans this term.
West Ham see the versatile midfielder as a star of the future and are keen to ensure he stays at the London Stadium for as long as possible.
However, convincing him to sign a new deal has proved problematic in the early stages of the 2018-19 campaign.
Reports claim Rice recently turned down a deal worth £40,000-a-week and it's understood he will get one final opportunity to accept West Ham's terms.
It's understood West Ham's previous offer contained a number of add-ons and his representatives are asking for a higher basic salary with fewer add-ons.
Rice, who also has a big decision to make on his international future with England and Republic of Ireland vying for his services, is currently contracted to West Ham until the summer of 2020.