The former Blackburn defender, who is now plying his trade in Turkey for Galatasaray, says Schwarzer would have benefited from such a switch.
The Australia international put in a masterful display to help the Socceroos secure a 0-0 draw in Friday's friendly against Switzerland in St Gallen.
"He is the ultimate professional," Neill said.
"He deserved to go to a club like Arsenal.
"But equally he will thrive under Mark Hughes at Fulham."
Schwarzer refused to comment publicly on the issue in the post-match press conference as the 37-year-old felt he might say something untoward.
"I would rather not say anything, I would really rather not say anything because otherwise I might say something wrong," he said.
The Gunners had two bids rejected before returning with a reported £4million deadline-day offer for the stopper which was rejected by the Craven Cottage outfit.
Meanwhile, goalkeeper David Stockdale has shown some impressive early season form for Fulham keeping Schwarzer on the bench.
Schwarzer will have to wait until the January transfer window before seeking his desired move across London.
The long-time Middlesbrough keeper said the current Australian camp in Europe could not have come at a better time.
"At the end of the day, you have to get on with your work and coming away with the national team was a great relief for me really," he said.