Matic began his second spell at Stamford Bridge on Wednesday after completing a transfer from Benfica reported by the Portuguese club to be worth £20.75million.
The 25-year-old left west London three years ago as part of the deal which saw David Luiz move from Benfica.
Chelsea boss Jose Mourinho views Matic as the defensive midfielder his team are missing and the Serbia international is keen to make an instant impact against United.
"The coach has to decide but I am ready. I'm in training, I played (for Benfica) on Sunday against Porto so I don't have any problems," Matic said.
United will arrive in the capital as champions but their chances of winning the title are as good as finished as they trail leaders Arsenal by 11 points.
Chelsea are only two points behind the Gunners, however, and could finish the weekend as leaders themselves if results go their way.
Matic believes the Blues will develop into a dominant force in Europe as well as England.
"Chelsea are a very good team and have very good young players. In the next few years Chelsea will show power," he said.
"Of course we need a bit of time because if a player is young he needs time to show all his qualities but I think Chelsea will be one of the best teams in Europe."