The 57-year-old music mogul stars alongside David on 'Britain's Got Talent' and the 45-year-old comedian has claimed Simon is frustrated to have not already been bestowed with the prestigious honour by the royal family.
He said: ''Simon definitely thinks he should have a knighthood. I don't know why, I don't know what he thinks he's done. Maybe by just being famous for long enough.
''What he doesn't realise is you have to do something positive, you can't just spread evil and think that you'll get one. So I think he's a bit peeved about it.''
But David is relieved it hasn't happened yet, because he is dreading the prospect of referring to the TV star as Sir Simon, which would become his official title if he were knighted.
David reflected: ''I think he thinks he was going to get one at one stage. Who knows, though it would be annoying to have to call him Sir Simon. I wouldn't like that, so I really hope it doesn't happen.''
Simon, on the other hand, has claimed David is ''furious'' at having previously been overlooked for an OBE, before going on an ''all-out assault this year'' to secure the prestigious accolade.
Simon said: ''He's gone on an all-out assault this year to suck up to as many people as possible so that he can get there before me, and he probably will.''
Meanwhile, fellow 'Britain's Got Talent' judge Alesha Dixon also joked that it would be a ''nightmare'' if David was awarded an OBE.
She quipped: ''When he won best judge at the National TV Awards, he reminded us of it every day.
''So can you imagine what would happen if he became an OBE? It would be a nightmare because he would make sure that we all knew, he'd probably wear the medal every single day just to rub it in our faces, just in case we forgot, because he's very competitive.''
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