Rice's current deal runs until 2028, with Arsenal holding a club option to extend it by a further year, but the champions want fresh terms in place well before either date arrives, in line with the policy that has already delivered a new contract for head coach Mikel Arteta.
Arsenal are using the September international break to finalise details, with talks expected to intensify this week.
The 27-year-old is set to be rewarded with a significant pay rise on a new five-year deal reported to be worth around £280,000 a week, which would keep him at the Emirates until 2031.
Arsenal paid West Ham United £105 million for Rice in the summer of 2023, and he has been a first-team fixture ever since, playing a central role in last season's Premier League title win, the club's first since 2004.
Ben White is also due to sit down with the club over an extension of his own, with two years left on his current terms.
Arsenal's business away from the pitch has picked up pace since Arteta agreed his new contract, as the club looks to secure the futures of the players considered central to its title defence.