The 32-year-old hasn’t featured for the Gunners since March and was omitted from their Premier League and Europa League squads this season.
Ozil responded to his latest snub by accusing the club of lacking loyalty as he vowed to keep fighting for his place in the side.
Arteta has since reiterated that the decision to omit the German is based on footballing reasons and not his refusal to take a pay cut.
Speaking ahead of Leicester’s clash against Arsenal at the Emirates on Sunday, Rodgers admitted that he too would drop Ozil as he doesn’t offer the defensive work rate that the modern game requires.
Asked whether there is a degree of a sadness that the playmaker is not being involved, Rodgers said: ‘Not really, I’d be very much like Mikel.
‘Ozil’s a talented player, but it depends on your structure. We need every player to contribute to the defensive aspect of the game as well as the attacking aspect.
‘The team have to operate with one brain. They have to function and work together. There will be teams where there is more freedom, but less structure.
‘Ozil’s a wonderful talent and very creative, absolutely. He can make the last pass, but it’s about the team. It’s about marrying the individual qualities of the player into the team and if you feel that player can’t press the game or doesn’t want to press the game, it has an effect on your attacking structure and your defensive structure.
‘If one person doesn’t do their job, then you can suffer. He’s a talent, but, as always with talent, you have to be a working talent.’
The Foxes boss added: ‘I always say to my attacking players, “Don’t run forward if you can’t run back”.
‘You have to be able to do the dirty work. This is the highest level of the game and, at that level, you have to be able to do both sides. You think of any top team in the world and you think of some of the attacking players.
‘If you look at Bayern Munich, the current European champions, and you look at Serge Gnabry and Thomas Muller, for instance, the guys that play down the sides. Look at how hard they work.
‘Look at Liverpool with Roberto Firmino and Sadio Mane – the work he puts in. That’s what you have got to do. You can’t carry anyone.’