The Swede left Arsenal last week as he seeks a managerial post.
And former Southend United manager Campbell made the shock revelation while testing out Marvel's new Avengers game with fellow his fellow Invincibles.
As soon as Campbell logged on, Robert Pires said: "I have a question for you Sol because Freddie is leaving.
"Are you interested in the job working with staff and Arteta or not?"
Without hesitation, Campbell replied: "Yes, I would. If something came up, I would. I would love to.
"Put my name forward and I will be there."
Pires laughed as he responded: "I will send a message to Edu."
Campbell quit as manager of Southend United in June after his team were relegated from League One.