Gunners bosses are set to slap a £50million price tag on the 22-year-old ahead of the summer transfer window, according to the Daily Mail.
Juventus are interested in snapping up Bellerin and are reportedly plotting a summer swoop.
But former Arsenal midfielder Parlour believes it would be foolish to cash in.
“I’d be amazed if Arsenal sold Bellerin,” he told talkSPORT.
“He’s still a young player, he’s still learning and he wants to learn.
“I still think defensively he has to get better, but he can get better.
“He’s not had the greatest of seasons and I think he’d be the first to admit that, but I do rate him a lot.
“I wouldn’t take £50m for him, because you’ve still got to replace him in the team.
“Full-backs these days are so hard to find, because they’ve got to be able to play like wingers.
“You’ve got to be able to get up the pitch and produce good quality.
“He’s got great pace, so I wouldn’t be selling him, no.”
Bellerin is under contract at Arsenal until the summer of 2023 after putting pen to paper on a long-term deal in November 2016.
He was a part of Barcelona’s academy before joining Arsenal in 2011.
The Spain international has represented his country three times since establishing himself as a Gunners regular.
Bellerin has previously been linked with Barcelona and Manchester City.