The Gunners have been linked with a surprise swoop to sign the Belgium international in the summer transfer window.
The Belgian star will be available on a free transfer given his current deal with the Red Devils will expire in the coming weeks.
Fellaini has been a controversial figure at Old Trafford given his unflattering style of play.
However, Manchester United boss Jose Mourinho has found a use for the 30-year-old as a defensive-minded player to frustrate their top-four rivals.
Arsenal have appointed former Sevilla boss Unai Emery as their new manager after Arsene Wenger called time on his 22 seasons in charge at the Emirates Stadium last month.
The Gunners have already added 34-year-old Switzerland international Stephan Lichtsteiner to their squad in a free transfer from Serie A giants Juventus.
Former Arsenal star Parlour believes Fellaini would be a good signing due to his ability to offer something different to the Gunners team.
“I never really know what his best position is. He’s played as an attacking midfielder and then a holding midfielder,” Parlour told Sky Sports.
“When you look at a free transfer he’s something different. Even if he didn’t start you could bring him off the bench.
“If you’re chasing a goal you might need to play a different style of football go a little bit more direct up to the front and he’s perfect for that. ‘Certainly he’s a player where you can change the system of play. You’d say that’s a decent signing.”
Fellaini moved to Manchester United in a £27m deal from Everton in the 2013 summer transfer window.
The Red Devils finished in second place in the Premier League table last term.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news