Arnold, who will steer the Sky Blues in Wednesday night's game against Premier League giants Liverpool at ANZ Stadium, has just completed his third season in charge.
He has a contract for the next two seasons and Barlow told The World Game he could see the 53-year-old eventually doubling that five-year stay, taking him through to the end of the 2023-24 season at least.
"There's absolutely no reason Graham can't become a 10-year coach here," Barlow said.
"He's been outstanding all season from a coaching perspective, but also from all of the other aspects of what Graham does, with his leadership and his work in the media and his mentoring of young players.
"He really has been incredible this season and he's very happy here and we're very happy with him, so I don't see that changing."
Sydney had eight coaches in their first nine seasons - Pierre Littbarski, Terry Butcher, Branko Culina, John Kosmina, Vitezslav Lavicka, Ian Crook, Steve Corica and Frank Farina.
They badly needed to find the right man to take them forward at the end of the 2013-14 season and Arnold was chosen.
He took them to the grand final in season 2014-15, but they lost to Melbourne Victory. In the season just gone, Sydney produced the greatest A-League campaign by any club, running away with the Premier's Plate and then beating Victory in a gripping grand final that went all the way to a penalty shootout.
Barlow said stability was crucial to the club continuing to be successful.
"But you can't have stability just for the sake of stability, you have to have the right people in the right roles and then stability to follow on from that and I think that's what we've achieved," he said.
"We've had real stability at ownership level, real stability at board level, at management level and coaching level and I think the consistency of the strategy and the consistency of the team effort is really starting to pay dividends and I think that will only continue.
"Graham has always been a terrific coach. He was quite critical of himself for the season previous to this one and talks a lot about how he has addressed those things. For me, he's always been a terrific coach and this season it just really came together and we had great success."
Sydney recently announced a new 10-year lease at their home ground, Allianz Stadium.
Barlow said the club will be aiming to increase average crowd figures to 35,000 over that time.
"Our average crowds this year were 18,000, we're the biggest tenant of the stadium and next year I've got every confidence the average crowds will be 20,000 or north of that," he said.
"Longer term, I believe the club is only at 50 per cent of what it will be, so we think we can achieve regular home crowds of 30,000 to 35,000 over the course of this 10-year lease.
"There's so much great potential for this club. We're only 12 years old and we're still in the beginning of this journey, and there's no question that this club can be a massive football club, both by Australian standards but also a big club within the Asia-Pacific region as well, so that's our goal."
They Sky Blues are currently on the hunt to find the right replacement for departing CEO Tony Pignata.
Barlow wouldn't be drawn on who the candidates are but confirmed the appointment will be finalised within the coming weeks.
"Tony has been with us for five years and has done a terrific job around growing the commercial aspects of the club," he said.
"But now we enter a new phase of our growth and I really believe the club will go to another level next season.
"We're in the recruitment process at the moment to find the right person to take us to that next level and we'll be in a position to announce that in the coming four or five weeks."
