The 19-year-old, who is a product of the clubs impressive academy, is yet to start for the first team this season but is considered to have a bright future at the club.
Manager Jim Magilton told the clubs website: "It's great news for Danny and great news for this football club.
"He has made massive strides over the last 12 months.
He has seen the benefits of what hard work can achieve in football and we know there is a lot more to come from him.
"He deserves his contract and now he needs to put that in his bottom drawer and come back to me in a year or so and say to me I'm a regular in your side and now I want to talk about an improved deal."