The former Manchester City title-winning manager stepped down as Italy boss in August just two years after lifting the Euros.
Mancini reportedly put pen to paper on a staggering £77million deal that runs for three years.
The 58-year-old approached Di Canio to offer him a role as a coach but the West Ham legend turned it down.
He explained to La Stampa why he rejected the job, saying: “I didn’t just say no to oil money, because it would have been an important experience in an environment that wants to grow and establish itself, like I do myself.
“Mancini didn’t offer me a minor role, he wanted me as a second coach on the pitch to train and improve the players.
“His courtship made me proud, especially given that we aren’t particularly close: a few games of padel, a chat and not a lot more, so if he thought about me, it’s because he believes in my ideas and my work.
“I want to thank him, it wasn’t easy to decide. I contemplated it for a long time and in the end I chose to follow my heart.”
Di Canio has not been a coach since managing Sunderland in 2013.
He guided the club to Premier League safety before being reportedly sacked due to a training ground bust-up with his players just five games into the new season.
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The controversial Italian also managed Swindon two years previously, firing them to the League Two title.
Di Canio played for Lazio, Juventus, Napoli, AC Milan and Celtic during his playing days.
But he best remembered for his time at West Ham, where he scored 51 goals in 141 games.
Saudi Arabia are without a win in their four matches since Mancini took to the dugout.
