The England international will enter the final year of his contract at the Etihad Stadium in the summer and the Citizens are working hard to tie the 24-year-old down to fresh terms before his value decreases.
However, talks are thought to have been going on for months and yet no deal has yet been agreed to extend Sterling's stay.
His current deal is believed to be worth around £170,00 a week and he wants to become one of City's best-paid players, with a rise to a basic of at least £220,000.
Manager Pep Guardiola has stated he is keen to keep Sterling at the club as he plays an important part of his plans going forward.
Guardiola said: "It's well-known we're delighted with him and would like him to continue. My club knows my opinion and we share that. After that it is the club and the agent."