The England international has reportedly offered the 16-year-old a VIP trip to Old Trafford to watch the Red Devils in action, according to The Sun.
Rooney tweeted to Stephenson: "Your story inspires me, reminds me of a friend I know. Thank you for being brave and sharing your story. No matter what happens on Idol, music inspires people and you inspire people. Keep doing it, you will help a lot of people."
The teenager replied: "OMG! Dude. I can't believe you tweeted me. I'm glad I inspired you. I'm a soccer player and you inspire me."
Rooney lost his childhood family friend Stephen Johnson to the condition in September last year.