United go into Sunday’s clash at Old Trafford in top form following a superb 3-0 win over Tottenham on Monday and face a Gunners side who have recently lost star players Cesc Fabregas and Samir Nasri and lost 2-0 to Liverpool at home last week.
But Arsene Wenger’s men bounced back during the week with a morale-boosting come-from-behind over Udinese to qualify for the Champions League group stage and Giggs knows not to write the North Londoners off.
"Arsenal are still a quality team with quality players," he told the Manchester Evening News.
"On their day they can beat anyone in Europe. They've proved that for years and years now.
"OK, so they've got a few injuries and a couple of players have left. But they've still got so much quality there.
"They've got a great manager and Arsenal are a great club. So you never underestimate them."