The 27-year-old joined the Gunners from West Ham United in the summer of 2023 and has become one of the most important players in Arteta's squad.
Rice made 55 appearances in all competitions last season, scoring five goals and providing nine assists as Arsenal secured the Premier League title. He has continued his strong form this campaign, recording one goal and five assists in 15 appearances.
His existing contract runs until the summer of 2028, but discussions over an extension have been progressing. BBC Sport reported in October that the two parties were approaching an agreement, and Rice has now provided an encouraging update.
Speaking ahead of England's Nations League meeting with Spain, the midfielder confirmed that he hopes to have a new deal completed soon.
"A new contract is hopefully on the horizon soon, and I'm extremely lucky to be at a club like Arsenal, where the manager shows me so much trust and team-mates who put so much energy into me," Rice said, according to BBC Sport.
The comments underline his satisfaction with life in north London and his desire to continue working under Arteta.
Rice has become a central figure in Arsenal's midfield since his arrival from West Ham, combining defensive work with an increasing contribution in the final third.
His performances have also made him an established member of the England team. He has scored eight goals and provided eight assists in 81 senior international appearances.
Arsenal have made an impressive start to the Premier League season, collecting 27 points from their opening ten matches to lead the table, five points clear of Brighton.
Rice's expected extension would represent another important step in the club's efforts to retain the core of a squad that has developed into a title-winning side.
For the midfielder, the prospect of continuing at Arsenal is clearly an appealing one, with his own words suggesting that an agreement could be reached in the near future.