The Red Devils star is being linked with a potential move to the north London side in the summer transfer window.
Manchester United have been unable to tie down the Belgium international to a new deal with his current contract set to expire this summer.
Fellaini has been linked with a potential move to Serie A or Turkey on a regular basis over the past few months.
The Gunners have emerged as surprise contenders to sign Fellaini to bolster their midfield under new manager Unai Emery.
Fellaini has proven a controversial figure at Manchester United due to his unattractive style of play.
Former Chelsea FC defender Burley believes Arsenal boss Emery wants to sign Fellaini to add more power to his Gunners team.
“He is looking for bigger and stronger guys,” Burley told ESPN FC.
“He is really trying to toughen them up.”
Arsenal finished in sixth spot in the Premier League table last term to miss out on a Champions League spot in successive seasons.
The Gunners lost 3-0 to Premier League champions Manchester City in the League Cup final at Wembley back in February.
Arsenal manager Arsene Wenger stood down after 22 seasons in charge.
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