The Scotland defender, who made a £25million move from Celtic in 2019, has been a bright spark in an otherwise disappointing Premier League campaign for the Gunners.
Tierney scored in a 3-2 win over Benfica last week to help his side into the Europa League last 16 and Parlour, who won three titles with Arsenal revealed he is a big admirer of the 23-year-old left back.
He told talkSPORT: “I really like his attitude.
“He turns up every week, you can see the desire when he’s playing; he really wants to win every game.
“He gives 100 per cent and is fantastic down that left hand side. That’s where Arsenal are most dangerous, that’s where the deliveries come from into the box.
“He’s been a brilliant signing, and he’s a really good lad as well; he’s really down to earth.
“He could probably be the Arsenal captain in the future.”