The Spaniard signed a new six-and-a-half-year contract in 2016, but continues to be linked with a departure from the Emirates Stadium.
Juventus are reported to have joined the chase for Bellerin, while a possible move to Barcelona has been mooted for some time.
Recent reports claimed that the Gunners would be willing to part ways with the 22-year-old for £50m, but Parlour believes that they would be making a huge mistake.
"I'd be amazed if Arsenal sold Bellerin," the former Gunners midfielder 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 has made 151 appearances for Arsenal since making his debut in 2013.