Fellaini had reportedly been close to agreeing a deal with AC Milan, before the move slowed down over his demands for a contract worth approximately €120,000-per-week after tax.
Juillard told followers on social media that Fellaini will meet with Arsenal reps "at the beginning of the week".
The Belgium worldwide is out of contract at Manchester United this summer and has so far rejected offers of an extension.
Since joining Utd from Everton for £29 million in 2013, the 30-year old has scored 20 goals in over 100 club appearances.
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While United want to sign him to a new contract―manager Jose Mourinho is a fan of the Belgian―the former Everton man has made a decision to keep his options open as he wants to be a regular starter.
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According to The Times, Arsenal have scheduled talks with Fellaini for Wednesday.
"He's not what you'd call a playmaker, where would they play him?"
"He knows I want him to stay, the club wants him to stay", Mourinho had said last month."He has an offer from us and it's up to him to say yes or no".