Monreal joined the Gunners from Malaga on deadline day and went straight into the team to face Stoke last weekend.
The Spanish international full-back helped Arsenal keep a clean sheet and Vermaelen believes that the 26-year-old will prove to be a shrewd purchase.
He told Sky Sports News: "He only had one training session with us I think but he came in and did really well.
"You can see he's quality. I think he will be a great signing for us."
Vermaelen missed the Stoke match with an ankle injury and is unlikely to play for Belgium this week despite reporting for international duty.