His Take That bandmate Barlow has been linked with the honour due to his work for next month's Diamond Jubilee.
While promoting Sunday's Soccer Aid, Williams told The Mirror: "Gary Barlow's sailing straight to a knighthood. You can just tell, can't you?
"Well, at some point people have got to look at this and see what I've done and say, oh yeah.
"He's gonna get it. It'll be Sir Gaz before Sir Robbie. Subconsciously it's a bit of a competition."
Barlow played down the speculation earlier this week, claiming he was "too young" to be knighted.
Williams, 38, recently confirmed that he is expecting a baby girl with wife Ayda Field.