When the academy graduate penned a five-year deal in July 2019, the playmaker had not made his Premier League debut for the Blues.
However, the 22-year-old has since contributed 17 goals and 16 assists from 116 appearances, playing a key role as Chelsea won the Champions League last season.
According to Goal, the Blues want to reward Mount for his rapid progression by handing him a contract extension and a significant pay-rise.
While the England international is tied to Stamford Bridge until the end of the 2023-24 campaign, Chelsea will want to avoid any transfer speculation regarding his future.
The club's hierarchy will also want to ensure that Mount feels appreciated at a time they are negotiating fresh terms with several other players.