The Gunners fullback had an up and down campaign in 2016/17 and was even dropped by manager Arsene Wenger.
"No, no (he didn't have a great season), you get that with young players," Parlour told talkSPORT.
"I think (Alex) Iwobi has been the same, he started really well but he's going to have that little bit of a dip during the season.
"They're young, they're learning and I think mentally it can do you as well.
"I think Bellerin was similar, obviously he has signed a long-term contract with Arsenal.
"He's a player that on his day is very good, we know that he's got pace.
"He's just got to probably learn a little bit better with the final pass.
"But he's a top talent and I can see why Barcelona would be interested in him."