The 23-year-old is believed to be considering an exit from the Emirates after reportedly deciding against signing a new contract, which is thought to have alerted Premier League champions Manchester City.
"If you're spending £75,000 a week on a player then you need him to be consistent, he needs to be one of your main players," Robson told talkSPORT. "I'm not sure Theo Walcott is that player.
"He's been too inconsistent during his time at Arsenal. Is he getting better? Is he going to be a top-class player? I'm not so sure.
"Arsenal could get a bit of money for him now. I don't think Walcott will be missed if he leaves. If I was the manager or on the board, I'd be looking to sell him anyway because I don't think he's improved during the time he's been at Arsenal."