The phrase "avoid noticing" is correct and usable in written English.
It can be used when discussing the act of deliberately not paying attention to something or choosing to overlook it.
Example: "In order to maintain peace during the argument, she decided to avoid noticing the tension in the room."
Alternatives: "ignore" or "overlook".
It's impossible to avoid noticing that they are all — every man and each woman — physically beautiful.
* It's hard to avoid noticing that conventional publishers were the best-represented stakeholders in the Finch Group.
The Liberty and the Indiana Fever could not avoid noticing the changes that took place yesterday at Madison Square Garden.
Show observers couldn't avoid noticing how the Ford and Dodge tag-team made Chevy's conservative new Silverado look about as gutsy as a Toyota Camry.
It was impossible for anyone who listened to avoid noticing the range of ethnicities and nationalities on that long, long list.
Yet it's worth looking directly at what's hard to avoid noticing — that most of the Hollywood personalities whom Wilson heard about and whose arrogant, aggressive, and uninhibited ways he found noteworthy were Jews.
He could not have avoided noticing that there were many religious traditions that claimed to report divine revelations, and that each in turn rested its claims on its own authority as a reliable witness to earlier historical events and their interpretation.
It's also the elephant in the center of the living room, cunning in its ability to avoid notice.
Each night, when the museum guards lock up for the day, they hide in bathroom stalls, standing on toilets to avoid notice.
"Each of the hijackers, apparently purposely selected to avoid notice, came easily and lawfully from abroad," Louis J. Freeh, the former director of the F.B.I., testified to Congress in October 2002.
A group of young men quickly gathered around the card table, and I slipped in behind the last few, crouching a little to avoid notice.
