The Spaniard has been linked with the top job at Arsenal, where he finished his playing career between 2011 and 2016:
After hanging up his boots, Arteta moved to City to work under Pep Guardiola following his appointment as Sky Blues manager.
He has been part of the coaching staff that has engineered record-breaking back-to-back Premier League title wins.
Despite the 37-year-old's success at the Etihad Stadium, De Bruyne believes City should allow Arteta to move on if he does get an opportunity elsewhere, per Goal:
"He came here three years ago and had to find his way a little bit, because to transition from player to coach is a little bit different. He is finding his role really, really good right now. I guess one day he will want to be a head coach—I don't know when, but he's helping the team in the way he thinks he can help, and is doing a good job.
"He is helping us a lot, but if he gets a good opportunity to be a head coach, and he thinks it's time for him to take that, I think as a club you need to let somebody go. You want to grow as a head coach."
Unai Emery was sacked as Gunners boss at the end of November, 18 months on from succeeding Arsene Wenger in the top job at the Emirates Stadium.
The Spaniard left with Arsenal sitting eighth in the Premier League table, eight points behind the top four and 19 off leaders Liverpool.
It is clear Ljungberg is not the long-term solution, and Arsenal would do well to install a new permanent manager sooner rather than later.
The busy Christmas period will be vital for the Gunners if they are to have any chance of qualifying for Europe next season.