The pair are yet to start together in a game since Rice sealed a British record £105 million from West Ham United.
Rice has featured in each of Arsenal's last two pre-season friendlies against the MLS All-Stars and Manchester United, starting in the latter and coming off the bench in the former.
Partey equally joined Arsenal’s pre-season squad last week and made a cameo appearance in their defeat to Manchester United at the weekend.
The Ghana international has, however, been linked with a move away from the Gunners following a summer of speculations.
Reacting to questions over Partey’s future, Arteta said he counts the midfielder as a key player and plans to play him alongside Rice.
“Thomas is a super important player for us and for me. I want him to be part of the team,” the Arsenal boss said.
“That’s for sure. Yeah. They can play together. That was in my plans… That’s why we bought Declan as well.”
Last month, there were reports that Partey could become the latest big name to move to Saudi Arabia after being linked with a move away from Arsenal.
He was said to be the subject of interest from some Saudi clubs, with Arsenal reportedly granting him permission to discuss a transfer.
According to a report by 90min, the Gunners were ready to allow the 30-year-old to leave if a concrete offer arrived this summer.
This came after European transfer expert Fabrizio Romano confirmed that Arsenal were looking to offload Partey.
Arteta’s latest comments, however, suggest the former Atletico Madrid man could be staying at the Emirates.