Yahoo Sport say the Gunners made an offer to the Manchester United boss after his sacking from Chelsea.
In fact, Mourinho had a number of proposals and United almost lost him because of their insistence on sticking with Louis van Gaal.
Everton, Inter Milan, Real Madrid and Roma also all came knocking.
In the end Mourinho was appointed as United boss just four days after Van Gaal finally got the axe for missing out on Champions League football.
However, at the weekend Mourinho became the first United manager to win silverware in his maiden year at the helm.
While the top brass at Old Trafford will be pleased with that win, Mourinho will be judged on his ability to challenge in the Champions League and Premier League in the long run.