Trade rumors involving Rondo have swirled since the Celtics selected point guard Marcus Smart with their first-round pick in this year's draft, with Rondo set to become a free agent after this season.
In September, Celtics president Danny Ainge said it was still possible Rondo could be traded but insisted he wanted to keep the four-time All-Star.
"I think [Rondo] wants to stay [in Boston]. We talk on the regular, I think he should stay," said Perkins.
Perkins and Rondo were teammates on the Celtics before Perkins was traded to Oklahoma City during the 2010-11 season.
Rondo broke his hand in September but returned in time to start the Celtics' season opener. In five games this season, the 28-year-old is averaging nine points, 11.2 assists and 1.6 steals.
Last season, Rondo averaged 11.7 points, 9.8 assists and 5.5 rebounds in 30 games after returning from a torn ACL.
The Thunder (2-6) play the Celtics (3-3) in Boston on Wednesday.
- Molly Geary